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Mathbox for Richard Penner |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege44 | Structured version Visualization version GIF version |
Description: Similar to a commuted pm2.62 424. Proposition 44 of [Frege1879] p. 47. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege44 | ⊢ ((¬ 𝜑 → 𝜓) → ((𝜓 → 𝜑) → 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege43 38458 | . 2 ⊢ ((¬ 𝜑 → 𝜑) → 𝜑) | |
2 | frege21 38438 | . 2 ⊢ (((¬ 𝜑 → 𝜑) → 𝜑) → ((¬ 𝜑 → 𝜓) → ((𝜓 → 𝜑) → 𝜑))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ((¬ 𝜑 → 𝜓) → ((𝜓 → 𝜑) → 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-frege1 38401 ax-frege2 38402 ax-frege8 38420 ax-frege28 38441 ax-frege31 38445 ax-frege41 38456 |
This theorem is referenced by: frege45 38460 |
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