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Mirrors > Home > NFE Home > Th. List > ax12v | GIF version |
Description: A weaker version of ax-12 1925 with distinct variable restrictions on pairs x, z and y, z. In order to show that this weakening is adequate, this should be the only theorem referencing ax-12 1925 directly. (Contributed by NM, 30-Jun-2016.) |
Ref | Expression |
---|---|
ax12v | ⊢ (¬ x = y → (y = z → ∀x y = z)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-12 1925 | 1 ⊢ (¬ x = y → (y = z → ∀x y = z)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1540 |
This theorem was proved from axioms: ax-12 1925 |
This theorem is referenced by: ax12o 1934 |
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