Theorem ax12dgen2 1726

Description: Degenerate instance of ax-12 1925 where bundled variables x and z have a common substitution. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 13-Apr-2017.)

Assertion

Ref	Expression
ax12dgen2	⊢ (¬ x = y → (y = x → ∀x y = x))

Proof of Theorem ax12dgen2

Step	Hyp	Ref	Expression
1		equcomi 1679	. 2 ⊢ (y = x → x = y)
2		pm2.21 100	. 2 ⊢ (¬ x = y → (x = y → ∀x y = x))
3	1, 2	syl5 28	1 ⊢ (¬ x = y → (y = x → ∀x y = x))

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

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675

This theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by: (None)