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Mirrors > Home > MPE Home > Th. List > pm2.61 | Structured version Visualization version GIF version |
Description: Theorem *2.61 of [WhiteheadRussell] p. 107. Useful for eliminating an antecedent. (Contributed by NM, 4-Jan-1993.) (Proof shortened by Wolf Lammen, 22-Sep-2013.) |
Ref | Expression |
---|---|
pm2.61 | ⊢ ((𝜑 → 𝜓) → ((¬ 𝜑 → 𝜓) → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.6 194 | . 2 ⊢ ((¬ 𝜑 → 𝜓) → ((𝜑 → 𝜓) → 𝜓)) | |
2 | 1 | com12 32 | 1 ⊢ ((𝜑 → 𝜓) → ((¬ 𝜑 → 𝜓) → 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem is referenced by: bnj1109 32329 jath 33237 isltrn2N 37746 ltrnid 37761 ltrneq 37775 onfrALT 41691 onfrALTVD 42033 |
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