How to prove an implication

[Dan Christensen]

How to prove the implication P => Q: Do either of the following.

1. Conditional proof: Assume P is true. Then prove that Q must also be true.
   
2. Proof by contrapositive: Assume Q is false (~Q). Then prove that P must also be false (~P).
   
3. Assume P is true and Q is false (P & ~Q). Then, for any proposition R, obtain a contradiction of the form R is true and R is false (R &  ~R). Or, equivalently, obtain R is true if and only if R is false (R <=> ~R).
   
4. Prove Q must be true.
   
5. Prove P must be false.
   

Did I miss any?  

Dan