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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege43 | Structured version Visualization version GIF version |
Description: If there is a choice only between 𝜑 and 𝜑, then 𝜑 takes place. Identical to pm2.18 121. Proposition 43 of [Frege1879] p. 47. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege43 | ⊢ ((¬ 𝜑 → 𝜑) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege42 37160 | . 2 ⊢ ¬ ¬ (𝜑 → 𝜑) | |
2 | frege40 37157 | . 2 ⊢ (¬ ¬ (𝜑 → 𝜑) → ((¬ 𝜑 → 𝜑) → 𝜑)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ((¬ 𝜑 → 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 37104 ax-frege2 37105 ax-frege8 37123 ax-frege28 37144 ax-frege31 37148 ax-frege41 37159 |
This theorem is referenced by: frege44 37162 |
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