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| Mirrors > Home > MPE Home > Th. List > mtand | Structured version Visualization version GIF version | ||
| Description: A modus tollens deduction. (Contributed by Jeff Hankins, 19-Aug-2009.) |
| Ref | Expression |
|---|---|
| mtand.1 | ⊢ (𝜑 → ¬ 𝜒) |
| mtand.2 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
| Ref | Expression |
|---|---|
| mtand | ⊢ (𝜑 → ¬ 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mtand.1 | . 2 ⊢ (𝜑 → ¬ 𝜒) | |
| 2 | mtand.2 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
| 3 | 2 | ex 412 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) |
| 4 | 1, 3 | mtod 198 | 1 ⊢ (𝜑 → ¬ 𝜓) |
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