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| Mirrors > Home > MPE Home > Th. List > pm2.21i | Structured version Visualization version GIF version | ||
| Description: A contradiction implies anything. Inference associated with pm2.21 123. Its associated inference is pm2.24ii 120. (Contributed by NM, 16-Sep-1993.) |
| Ref | Expression |
|---|---|
| pm2.21i.1 | ⊢ ¬ 𝜑 |
| Ref | Expression |
|---|---|
| pm2.21i | ⊢ (𝜑 → 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | pm2.21i.1 | . . 3 ⊢ ¬ 𝜑 | |
| 2 | 1 | a1i 11 | . 2 ⊢ (¬ 𝜓 → ¬ 𝜑) |
| 3 | 2 | con4i 114 | 1 ⊢ (𝜑 → 𝜓) |
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