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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 140 | . 2 ⊢ (𝜒 → ¬ 𝜑) |
4 | 3 | con2i 141 | 1 ⊢ (𝜑 → ¬ 𝜒) |
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