Theorem ax12w 1724

Description: Weak version (principal instance) of ax-12 1925. (Because y and z don't need to be distinct, this actually bundles the principal instance and the degenerate instance (-. x = y -> (y = y -> A.xy = y)).) Uses only Tarski's FOL axiom schemes. The proof is trivial but is included to complete the set ax6w 1717, ax7w 1718, and ax11w 1721. (Contributed by NM, 10-Apr-2017.)

Assertion

Ref	Expression
ax12w	|- (-. x = y -> (y = z -> A.x y = z))

Distinct variable groups:   x,y   x,z

Proof of Theorem ax12w

Step	Hyp	Ref	Expression
1		a17d 1617	1 |- (-. x = y -> (y = z -> A.x y = z))

This proof depends on syntax axioms:  -. wn 3   -> wi 4  A.wal 1540

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-17 1616

This theorem is used by: (None)