Helping Wonky Man so much doesn't feel right. A student
should do his homework on his own to learn something. 
Ok, one more piece of the puzzle revealed, this theorem:
Theorem specialize to b
37	ALL(x):ALL(r):ALL(b):ALL(y):ALL(z):[x=b => 
[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => 
x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
	Rem DNeg, 36
Proved from Theorem specialize to r and Theorem swap
---------------------------- begin proof --------------------------------------------------
Theorem specialize to r
1	ALL(x):ALL(r):ALL(b):ALL(y):ALL(z):[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
	Axiom
Theorem swap
2	ALL(x):ALL(b):ALL(r):ALL(y):ALL(z):[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]
	=> [[x=b | x=r] & [y=b | y=r] & [z=b | z=r] => x=b & y=b | x=r & y=r | [x=b & z=b | x=r & z=r] | [y=b & z=b | y=r & z=r]]]
	Axiom
	3	~ALL(x):ALL(r):ALL(b):ALL(y):ALL(z):[x=b => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
		Premise
	4	~ALL(x):ALL(r):ALL(b):ALL(y):~EXIST(z):~[x=b => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
		Quant, 3
	5	~ALL(x):ALL(r):ALL(b):~EXIST(y):~~EXIST(z):~[x=b => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
		Quant, 4
	6	~ALL(x):ALL(r):~EXIST(b):~~EXIST(y):~~EXIST(z):~[x=b => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
		Quant, 5
	7	~ALL(x):~EXIST(r):~~EXIST(b):~~EXIST(y):~~EXIST(z):~[x=b => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
		Quant, 6
	8	~~EXIST(x):~~EXIST(r):~~EXIST(b):~~EXIST(y):~~EXIST(z):~[x=b => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
		Quant, 7
	9	EXIST(x):~~EXIST(r):~~EXIST(b):~~EXIST(y):~~EXIST(z):~[x=b => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
		Rem DNeg, 8
	10	EXIST(x):EXIST(r):~~EXIST(b):~~EXIST(y):~~EXIST(z):~[x=b => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
		Rem DNeg, 9
	11	EXIST(x):EXIST(r):EXIST(b):~~EXIST(y):~~EXIST(z):~[x=b => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
		Rem DNeg, 10
	12	EXIST(x):EXIST(r):EXIST(b):EXIST(y):~~EXIST(z):~[x=b => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
		Rem DNeg, 11
	13	EXIST(x):EXIST(r):EXIST(b):EXIST(y):EXIST(z):~[x=b => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
		Rem DNeg, 12
	14	EXIST(r):EXIST(b):EXIST(y):EXIST(z):~[x=b => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
		E Spec, 13
	15	EXIST(b):EXIST(y):EXIST(z):~[x=b => [[x=u | x=b] & [y=u | y=b] & [z=u | z=b] => x=u & y=u | x=b & y=b | [x=u & z=u | x=b & z=b] | [y=u & z=u | y=b & z=b]]]
		E Spec, 14
	16	EXIST(y):EXIST(z):~[x=v => [[x=u | x=v] & [y=u | y=v] & [z=u | z=v] => x=u & y=u | x=v & y=v | [x=u & z=u | x=v & z=v] | [y=u & z=u | y=v & z=v]]]
		E Spec, 15
	17	EXIST(z):~[x=v => [[x=u | x=v] & [y=u | y=v] & [z=u | z=v] => x=u & y=u | x=v & y=v | [x=u & z=u | x=v & z=v] | [y=u & z=u | y=v & z=v]]]
		E Spec, 16
	18	~[x=v => [[x=u | x=v] & [y=u | y=v] & [z=u | z=v] => x=u & y=u | x=v & y=v | [x=u & z=u | x=v & z=v] | [y=u & z=u | y=v & z=v]]]
		E Spec, 17
	19	~~[x=v & ~[[x=u | x=v] & [y=u | y=v] & [z=u | z=v] => x=u & y=u | x=v & y=v | [x=u & z=u | x=v & z=v] | [y=u & z=u | y=v & z=v]]]
		Imply-And, 18
	20	x=v & ~[[x=u | x=v] & [y=u | y=v] & [z=u | z=v] => x=u & y=u | x=v & y=v | [x=u & z=u | x=v & z=v] | [y=u & z=u | y=v & z=v]]
		Rem DNeg, 19
	21	x=v
		Split, 20
	22	~[[x=u | x=v] & [y=u | y=v] & [z=u | z=v] => x=u & y=u | x=v & y=v | [x=u & z=u | x=v & z=v] | [y=u & z=u | y=v & z=v]]
		Split, 20
	23	ALL(r):ALL(b):ALL(y):ALL(z):[x=r => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
		U Spec, 1
	24	ALL(b):ALL(y):ALL(z):[x=v => [[x=v | x=b] & [y=v | y=b] & [z=v | z=b] => x=v & y=v | x=b & y=b | [x=v & z=v | x=b & z=b] | [y=v & z=v | y=b & z=b]]]
		U Spec, 23
	25	ALL(y):ALL(z):[x=v => [[x=v | x=u] & [y=v | y=u] & [z=v | z=u] => x=v & y=v | x=u & y=u | [x=v & z=v | x=u & z=u] | [y=v & z=v | y=u & z=u]]]
		U Spec, 24
	26	ALL(z):[x=v => [[x=v | x=u] & [y=v | y=u] & [z=v | z=u] => x=v & y=v | x=u & y=u | [x=v & z=v | x=u & z=u] | [y=v & z=v | y=u & z=u]]]
		U Spec, 25
	27	x=v => [[x=v | x=u] & [y=v | y=u] & [z=v | z=u] => x=v & y=v | x=u & y=u | [x=v & z=v | x=u & z=u] | [y=v & z=v | y=u & z=u]]
		U Spec, 26
	28	[x=v | x=u] & [y=v | y=u] & [z=v | z=u] => x=v & y=v | x=u & y=u | [x=v & z=v | x=u & z=u] | [y=v & z=v | y=u & z=u]
		Detach, 27, 21
	29	ALL(b):ALL(r):ALL(y):ALL(z):[[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]
		=> [[x=b | x=r] & [y=b | y=r] & [z=b | z=r] => x=b & y=b | x=r & y=r | [x=b & z=b | x=r & z=r] | [y=b & z=b | y=r & z=r]]]
		U Spec, 2
	30	ALL(r):ALL(y):ALL(z):[[x=r | x=u] & [y=r | y=u] & [z=r | z=u] => x=r & y=r | x=u & y=u | [x=r & z=r | x=u & z=u] | [y=r & z=r | y=u & z=u]
		=> [[x=u | x=r] & [y=u | y=r] & [z=u | z=r] => x=u & y=u | x=r & y=r | [x=u & z=u | x=r & z=r] | [y=u & z=u | y=r & z=r]]]
		U Spec, 29
	31	ALL(y):ALL(z):[[x=v | x=u] & [y=v | y=u] & [z=v | z=u] => x=v & y=v | x=u & y=u | [x=v & z=v | x=u & z=u] | [y=v & z=v | y=u & z=u]
		=> [[x=u | x=v] & [y=u | y=v] & [z=u | z=v] => x=u & y=u | x=v & y=v | [x=u & z=u | x=v & z=v] | [y=u & z=u | y=v & z=v]]]
		U Spec, 30
	32	ALL(z):[[x=v | x=u] & [y=v | y=u] & [z=v | z=u] => x=v & y=v | x=u & y=u | [x=v & z=v | x=u & z=u] | [y=v & z=v | y=u & z=u]
		=> [[x=u | x=v] & [y=u | y=v] & [z=u | z=v] => x=u & y=u | x=v & y=v | [x=u & z=u | x=v & z=v] | [y=u & z=u | y=v & z=v]]]
		U Spec, 31
	33	[x=v | x=u] & [y=v | y=u] & [z=v | z=u] => x=v & y=v | x=u & y=u | [x=v & z=v | x=u & z=u] | [y=v & z=v | y=u & z=u]
		=> [[x=u | x=v] & [y=u | y=v] & [z=u | z=v] => x=u & y=u | x=v & y=v | [x=u & z=u | x=v & z=v] | [y=u & z=u | y=v & z=v]]
		U Spec, 32
	34	[x=u | x=v] & [y=u | y=v] & [z=u | z=v] => x=u & y=u | x=v & y=v | [x=u & z=u | x=v & z=v] | [y=u & z=u | y=v & z=v]
		Detach, 33, 28
	35	~[[x=u | x=v] & [y=u | y=v] & [z=u | z=v] => x=u & y=u | x=v & y=v | [x=u & z=u | x=v & z=v] | [y=u & z=u | y=v & z=v]]
		& [[x=u | x=v] & [y=u | y=v] & [z=u | z=v] => x=u & y=u | x=v & y=v | [x=u & z=u | x=v & z=v] | [y=u & z=u | y=v & z=v]]
		Join, 22, 34
36	~~ALL(x):ALL(r):ALL(b):ALL(y):ALL(z):[x=b => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
	Conclusion, 3
37	ALL(x):ALL(r):ALL(b):ALL(y):ALL(z):[x=b => [[x=r | x=b] & [y=r | y=b] & [z=r | z=b] => x=r & y=r | x=b & y=b | [x=r & z=r | x=b & z=b] | [y=r & z=r | y=b & z=b]]]
	Rem DNeg, 36
---------------------------- end proof --------------------------------------------------