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| Mirrors > Home > MPE Home > Th. List > con3i | Structured version Visualization version GIF version | ||
| Description: A contraposition inference. Inference associated with con3 153. Its associated inference is mto 197. (Contributed by NM, 3-Jan-1993.) (Proof shortened by Wolf Lammen, 20-Jun-2013.) |
| Ref | Expression |
|---|---|
| con3i.a | ⊢ (𝜑 → 𝜓) |
| Ref | Expression |
|---|---|
| con3i | ⊢ (¬ 𝜓 → ¬ 𝜑) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | id 22 | . 2 ⊢ (¬ 𝜓 → ¬ 𝜓) | |
| 2 | con3i.a | . 2 ⊢ (𝜑 → 𝜓) | |
| 3 | 1, 2 | nsyl 140 | 1 ⊢ (¬ 𝜓 → ¬ 𝜑) |
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