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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege40 | Structured version Visualization version GIF version |
Description: Anything implies pm2.18 128. Proposition 40 of [Frege1879] p. 46. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege40 | ⊢ (¬ 𝜑 → ((¬ 𝜓 → 𝜓) → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege39 43150 | . 2 ⊢ ((¬ 𝜓 → 𝜓) → (¬ 𝜓 → 𝜑)) | |
2 | frege35 43146 | . 2 ⊢ (((¬ 𝜓 → 𝜓) → (¬ 𝜓 → 𝜑)) → (¬ 𝜑 → ((¬ 𝜓 → 𝜓) → 𝜓))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (¬ 𝜑 → ((¬ 𝜓 → 𝜓) → 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-frege1 43098 ax-frege2 43099 ax-frege8 43117 ax-frege28 43138 ax-frege31 43142 |
This theorem is referenced by: frege43 43155 |
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