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| Mirrors > Home > MPE Home > Th. List > nsyl | Structured version Visualization version GIF version | ||
| Description: A negated syllogism inference. (Contributed by NM, 31-Dec-1993.) (Proof shortened by Wolf Lammen, 2-Mar-2013.) |
| Ref | Expression |
|---|---|
| nsyl.1 | ⊢ (𝜑 → ¬ 𝜓) |
| nsyl.2 | ⊢ (𝜒 → 𝜓) |
| Ref | Expression |
|---|---|
| nsyl | ⊢ (𝜑 → ¬ 𝜒) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nsyl.1 | . . 3 ⊢ (𝜑 → ¬ 𝜓) | |
| 2 | nsyl.2 | . . 3 ⊢ (𝜒 → 𝜓) | |
| 3 | 1, 2 | nsyl3 138 | . 2 ⊢ (𝜒 → ¬ 𝜑) |
| 4 | 3 | con2i 139 | 1 ⊢ (𝜑 → ¬ 𝜒) |
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