Theorem ax12or 1522

Description: Alias for ax-i12 1521, 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 1521	1 ⊢ (∀𝑧 𝑧 = 𝑥 ∨ (∀𝑧 𝑧 = 𝑦 ∨ ∀𝑧(𝑥 = 𝑦 → ∀𝑧 𝑥 = 𝑦)))

Syntax hints:   → wi 4   ∨ wo 709  ∀wal 1362

This theorem was proved from axioms:  ax-i12 1521

This theorem is referenced by:  ax12  1526  hbequid  1527  hbae  1732  equvini  1772  equveli  1773  dveeq2  1829  dveeq2or  1830  dvelimALT  2029  dvelimfv  2030