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Mirrors > Home > MPE Home > Th. List > pm2.65da | Structured version Visualization version GIF version |
Description: Deduction for proof by contradiction. (Contributed by NM, 12-Jun-2014.) |
Ref | Expression |
---|---|
pm2.65da.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
pm2.65da.2 | ⊢ ((𝜑 ∧ 𝜓) → ¬ 𝜒) |
Ref | Expression |
---|---|
pm2.65da | ⊢ (𝜑 → ¬ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.65da.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
2 | 1 | ex 416 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) |
3 | pm2.65da.2 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → ¬ 𝜒) | |
4 | 3 | ex 416 | . 2 ⊢ (𝜑 → (𝜓 → ¬ 𝜒)) |
5 | 2, 4 | pm2.65d 199 | 1 ⊢ (𝜑 → ¬ 𝜓) |
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