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Mirrors > Home > MPE Home > Th. List > jarl | Structured version Visualization version GIF version |
Description: Elimination of a nested antecedent as a partial converse of ja 172 (the other being jarr 104). (Contributed by Wolf Lammen, 10-May-2013.) |
Ref | Expression |
---|---|
jarl | ⊢ (((𝜑 → 𝜓) → 𝜒) → (¬ 𝜑 → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.21 119 | . 2 ⊢ (¬ 𝜑 → (𝜑 → 𝜓)) | |
2 | 1 | imim1i 61 | 1 ⊢ (((𝜑 → 𝜓) → 𝜒) → (¬ 𝜑 → 𝜒)) |
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: pm2.68 425 merco2 1652 rp-fakeimass 36876 |
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