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| Mirrors > Home > MPE Home > Th. List > con3d | Structured version Visualization version GIF version | ||
| Description: A contraposition deduction. Deduction form of con3 153. (Contributed by NM, 10-Jan-1993.) |
| Ref | Expression |
|---|---|
| con3d.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
| Ref | Expression |
|---|---|
| con3d | ⊢ (𝜑 → (¬ 𝜒 → ¬ 𝜓)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | notnotr 130 | . . 3 ⊢ (¬ ¬ 𝜓 → 𝜓) | |
| 2 | con3d.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
| 3 | 1, 2 | syl5 34 | . 2 ⊢ (𝜑 → (¬ ¬ 𝜓 → 𝜒)) |
| 4 | 3 | con1d 145 | 1 ⊢ (𝜑 → (¬ 𝜒 → ¬ 𝜓)) |
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