Theorem ax12dgen3 1727

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

Assertion

Ref	Expression
ax12dgen3	⊢ (¬ x = y → (y = y → ∀x y = y))

Proof of Theorem ax12dgen3

Step	Hyp	Ref	Expression
1		equid 1676	. . 3 ⊢ y = y
2	1	ax-gen 1546	. 2 ⊢ ∀x y = y
3	2	2a1i 24	1 ⊢ (¬ x = y → (y = y → ∀x y = y))

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)