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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege61b | Structured version Visualization version GIF version |
Description: Lemma for frege65b 42661. Proposition 61 of [Frege1879] p. 52. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege61b | ⊢ (([𝑥 / 𝑦]𝜑 → 𝜓) → (∀𝑦𝜑 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-frege58b 42652 | . 2 ⊢ (∀𝑦𝜑 → [𝑥 / 𝑦]𝜑) | |
2 | frege9 42563 | . 2 ⊢ ((∀𝑦𝜑 → [𝑥 / 𝑦]𝜑) → (([𝑥 / 𝑦]𝜑 → 𝜓) → (∀𝑦𝜑 → 𝜓))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (([𝑥 / 𝑦]𝜑 → 𝜓) → (∀𝑦𝜑 → 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1540 [wsb 2068 |
This theorem was proved from axioms: ax-mp 5 ax-frege1 42541 ax-frege2 42542 ax-frege8 42560 ax-frege58b 42652 |
This theorem is referenced by: frege65b 42661 |
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