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Mirrors > Home > ILE Home > Th. List > pm2.01da | GIF version |
Description: Deduction based on reductio ad absurdum. (Contributed by Mario Carneiro, 9-Feb-2017.) |
Ref | Expression |
---|---|
pm2.01da.1 | ⊢ ((𝜑 ∧ 𝜓) → ¬ 𝜓) |
Ref | Expression |
---|---|
pm2.01da | ⊢ (𝜑 → ¬ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.01da.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → ¬ 𝜓) | |
2 | 1 | ex 114 | . 2 ⊢ (𝜑 → (𝜓 → ¬ 𝜓)) |
3 | 2 | pm2.01d 608 | 1 ⊢ (𝜑 → ¬ 𝜓) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 103 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia3 107 ax-in1 604 |
This theorem is referenced by: efrirr 4313 infnfi 6840 |
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