Theorem ax12or 1532

Description: Alias for ax-i12 1531, 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 1531	1 ⊢ (∀𝑧 𝑧 = 𝑥 ∨ (∀𝑧 𝑧 = 𝑦 ∨ ∀𝑧(𝑥 = 𝑦 → ∀𝑧 𝑥 = 𝑦)))

Syntax hints:   → wi 4   ∨ wo 710  ∀wal 1371

This theorem was proved from axioms:  ax-i12 1531

This theorem is referenced by:  ax12  1536  hbequid  1537  hbae  1742  equvini  1782  equveli  1783  dveeq2  1839  dveeq2or  1840  dvelimALT  2039  dvelimfv  2040