Hello,
by reading axext (
hol.mm theorem -
http://us.metamath.org/holuni/axext.html) and ax-ext (axiom
set.mm -
http://us.metamath.org/mpeuni/ax-ext.html),
ax-ext $a |- ( A. z ( z e. x <-> z e. y ) -> x = y ) $.
$d x y A $. $d x y B $. $d x y al $.
axext.1 $e |- A : ( al -> bool ) $.
axext.2 $e |- B : ( al -> bool ) $.
$( Axiom of Extensionality. An axiom of Zermelo-Fraenkel set theory. It
states that two sets are identical if they contain the same elements.
Axiom Ext of [BellMachover] p. 461. $)
axext $p |- T. |=
[ ( ! x : al . [ ( A x : al ) = ( B x : al ) ] ==> [ A = B ] $=
I have the impression that axext is not quite the HOL version of the extensionality axiom.
Indeed, for me alpha->star is not necessary a set but only a predicate. So alpha->star would not always be a set but it could be a class.
Also, ax-ext uses "=" and axext "<->". Is this difference important?
Most likely, I probably misunderstood one or more concepts.
Your help will be useful.
RC