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Mirrors > Home > MPE Home > Th. List > pm2.61i | Structured version Visualization version GIF version |
Description: Inference eliminating an antecedent. (Contributed by NM, 5-Apr-1994.) (Proof shortened by Wolf Lammen, 19-Nov-2023.) |
Ref | Expression |
---|---|
pm2.61i.1 | ⊢ (𝜑 → 𝜓) |
pm2.61i.2 | ⊢ (¬ 𝜑 → 𝜓) |
Ref | Expression |
---|---|
pm2.61i | ⊢ 𝜓 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.61i.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | pm2.61i.2 | . . 3 ⊢ (¬ 𝜑 → 𝜓) | |
3 | 1, 2 | nsyl4 161 | . 2 ⊢ (¬ 𝜓 → 𝜓) |
4 | 3 | pm2.18i 131 | 1 ⊢ 𝜓 |
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