Theorem ax12or 1508

Description: Alias for ax-i12 1507, 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 1507	1 ⊢ (∀𝑧 𝑧 = 𝑥 ∨ (∀𝑧 𝑧 = 𝑦 ∨ ∀𝑧(𝑥 = 𝑦 → ∀𝑧 𝑥 = 𝑦)))

Syntax hints:   → wi 4   ∨ wo 708  ∀wal 1351

This theorem was proved from axioms:  ax-i12 1507

This theorem is referenced by:  ax12  1512  hbequid  1513  hbae  1718  equvini  1758  equveli  1759  dveeq2  1815  dveeq2or  1816  dvelimALT  2010  dvelimfv  2011