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Mirrors > Home > NFE Home > Th. List > ax11wlem | GIF version |
Description: Lemma for weak version of ax-11 1746. Uses only Tarski's FOL axiom schemes. In some cases, this lemma may lead to shorter proofs than ax11w 1721. (Contributed by NM, 10-Apr-2017.) |
Ref | Expression |
---|---|
ax11wlemw.1 | ⊢ (x = y → (φ ↔ ψ)) |
Ref | Expression |
---|---|
ax11wlem | ⊢ (x = y → (φ → ∀x(x = y → φ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax11wlemw.1 | . 2 ⊢ (x = y → (φ ↔ ψ)) | |
2 | ax-17 1616 | . 2 ⊢ (ψ → ∀xψ) | |
3 | 1, 2 | ax11i 1647 | 1 ⊢ (x = y → (φ → ∀x(x = y → φ))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 176 ∀wal 1540 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 |
This theorem depends on definitions: df-bi 177 |
This theorem is referenced by: ax11w 1721 |
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