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| Mirrors > Home > MPE Home > Th. List > mtod | Structured version Visualization version GIF version | ||
| Description: Modus tollens deduction. (Contributed by NM, 3-Apr-1994.) (Proof shortened by Wolf Lammen, 11-Sep-2013.) |
| Ref | Expression |
|---|---|
| mtod.1 | ⊢ (𝜑 → ¬ 𝜒) |
| mtod.2 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
| Ref | Expression |
|---|---|
| mtod | ⊢ (𝜑 → ¬ 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mtod.2 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
| 2 | mtod.1 | . . 3 ⊢ (𝜑 → ¬ 𝜒) | |
| 3 | 2 | a1d 25 | . 2 ⊢ (𝜑 → (𝜓 → ¬ 𝜒)) |
| 4 | 1, 3 | pm2.65d 196 | 1 ⊢ (𝜑 → ¬ 𝜓) |
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