Theorem ax12or 1534

Description: Alias for ax-i12 1533, 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 1533	1 ⊢ (∀𝑧 𝑧 = 𝑥 ∨ (∀𝑧 𝑧 = 𝑦 ∨ ∀𝑧(𝑥 = 𝑦 → ∀𝑧 𝑥 = 𝑦)))

Syntax hints:   → wi 4   ∨ wo 712  ∀wal 1373

This theorem was proved from axioms:  ax-i12 1533

This theorem is referenced by:  ax12  1538  hbequid  1539  hbae  1744  equvini  1784  equveli  1785  dveeq2  1841  dveeq2or  1842  dvelimALT  2041  dvelimfv  2042