Theorem ax12or 1557

Description: Alias for ax-i12 1556, 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 1556	1 ⊢ (∀𝑧 𝑧 = 𝑥 ∨ (∀𝑧 𝑧 = 𝑦 ∨ ∀𝑧(𝑥 = 𝑦 → ∀𝑧 𝑥 = 𝑦)))

Syntax hints:   → wi 4   ∨ wo 716  ∀wal 1396

This theorem was proved from axioms:  ax-i12 1556

This theorem is referenced by:  ax12  1561  hbequid  1562  hbae  1766  equvini  1807  equveli  1808  dveeq2  1864  dveeq2or  1865  dvelimALT  2064  dvelimfv  2065