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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 = yxy = 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.)
Ref Expression
ax12w x = y → (y = zx y = z))
Distinct variable groups:   x,y   x,z

Proof of Theorem ax12w
StepHypRef Expression
1 a17d 1617 1 x = y → (y = zx y = z))
Colors of variables: wff setvar class
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)
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