Theorem ax12or 1501

Description: Alias for ax-i12 1500, 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 1500	1 ⊢ (∀𝑧 𝑧 = 𝑥 ∨ (∀𝑧 𝑧 = 𝑦 ∨ ∀𝑧(𝑥 = 𝑦 → ∀𝑧 𝑥 = 𝑦)))

Syntax hints:   → wi 4   ∨ wo 703  ∀wal 1346

This theorem was proved from axioms:  ax-i12 1500

This theorem is referenced by:  ax12  1505  hbequid  1506  hbae  1711  equvini  1751  equveli  1752  dveeq2  1808  dveeq2or  1809  dvelimALT  2003  dvelimfv  2004