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 → ∀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 → ∀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 → ∀x y = z))

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-17 1616

This theorem is referenced by: (None)