Theorem ax4sp1 2174

Description: A special case of ax-4 2135 without using ax-4 2135 or ax-17 1616. (Contributed by NM, 13-Jan-2011.) (Proof modification is discouraged.)

Assertion

Ref	Expression
ax4sp1	⊢ (∀y ¬ x = x → ¬ x = x)

Proof of Theorem ax4sp1

Step	Hyp	Ref	Expression
1		equidqe 2173	. 2 ⊢ ¬ ∀y ¬ x = x
2	1	pm2.21i 123	1 ⊢ (∀y ¬ x = x → ¬ x = 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-8 1675  ax-6o 2137  ax-9o 2138

This theorem is referenced by: (None)