Theorem ax12or 1496

Description: Alias for ax-i12 1495, to be used in place of it for labeling consistency. (Contributed by NM, 3-Feb-2015.)

Assertion

Ref	Expression
ax12or	⊢ (∀𝑧 𝑧 = 𝑥 ∨ (∀𝑧 𝑧 = 𝑦 ∨ ∀𝑧(𝑥 = 𝑦 → ∀𝑧 𝑥 = 𝑦)))

Proof of Theorem ax12or

Step	Hyp	Ref	Expression
1		ax-i12 1495	1 ⊢ (∀𝑧 𝑧 = 𝑥 ∨ (∀𝑧 𝑧 = 𝑦 ∨ ∀𝑧(𝑥 = 𝑦 → ∀𝑧 𝑥 = 𝑦)))

Syntax hints:   → wi 4   ∨ wo 698  ∀wal 1341

This theorem was proved from axioms:  ax-i12 1495

This theorem is referenced by:  ax12  1500  hbequid  1501  hbae  1706  equvini  1746  equveli  1747  dveeq2  1803  dveeq2or  1804  dvelimALT  1998  dvelimfv  1999