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| Mirrors > Home > MPE Home > Th. List > pm2.21d | Structured version Visualization version GIF version | ||
| Description: A contradiction implies anything. Deduction associated with pm2.21 123. (Contributed by NM, 10-Feb-1996.) |
| Ref | Expression |
|---|---|
| pm2.21d.1 | ⊢ (𝜑 → ¬ 𝜓) |
| Ref | Expression |
|---|---|
| pm2.21d | ⊢ (𝜑 → (𝜓 → 𝜒)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | pm2.21d.1 | . . 3 ⊢ (𝜑 → ¬ 𝜓) | |
| 2 | 1 | a1d 25 | . 2 ⊢ (𝜑 → (¬ 𝜒 → ¬ 𝜓)) |
| 3 | 2 | con4d 115 | 1 ⊢ (𝜑 → (𝜓 → 𝜒)) |
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