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Mirrors > Home > NFE Home > Th. List > ax12w | GIF version |
Description: Weak version (principal instance) of ax-12 1925. (Because y and z don't need to be distinct, this actually bundles the principal instance and the degenerate instance (¬ x = y → (y = y → ∀xy = y)).) Uses only Tarski's FOL axiom schemes. The proof is trivial but is included to complete the set ax6w 1717, ax7w 1718, and ax11w 1721. (Contributed by NM, 10-Apr-2017.) |
Ref | Expression |
---|---|
ax12w | ⊢ (¬ x = y → (y = z → ∀x y = z)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a17d 1617 | 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-mp 5 ax-1 6 ax-17 1616 |
This theorem is referenced by: (None) |
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