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Mirrors > Home > ILE Home > Th. List > ax12or | GIF version |
Description: Alias for ax-i12 1494, to be used in place of it for labeling consistency. (Contributed by NM, 3-Feb-2015.) |
Ref | Expression |
---|---|
ax12or | ⊢ (∀𝑧 𝑧 = 𝑥 ∨ (∀𝑧 𝑧 = 𝑦 ∨ ∀𝑧(𝑥 = 𝑦 → ∀𝑧 𝑥 = 𝑦))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-i12 1494 | 1 ⊢ (∀𝑧 𝑧 = 𝑥 ∨ (∀𝑧 𝑧 = 𝑦 ∨ ∀𝑧(𝑥 = 𝑦 → ∀𝑧 𝑥 = 𝑦))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∨ wo 698 ∀wal 1340 |
This theorem was proved from axioms: ax-i12 1494 |
This theorem is referenced by: ax12 1499 hbequid 1500 hbae 1705 equvini 1745 equveli 1746 dveeq2 1802 dveeq2or 1803 dvelimALT 1997 dvelimfv 1998 |
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