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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 412 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) |
| 3 | pm2.65da.2 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → ¬ 𝜒) | |
| 4 | 3 | ex 412 | . 2 ⊢ (𝜑 → (𝜓 → ¬ 𝜒)) |
| 5 | 2, 4 | pm2.65d 196 | 1 ⊢ (𝜑 → ¬ 𝜓) |
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