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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, 12-Sep-2013.) |
Ref | Expression |
---|---|
pm2.61i.1 | ⊢ (𝜑 → 𝜓) |
pm2.61i.2 | ⊢ (¬ 𝜑 → 𝜓) |
Ref | Expression |
---|---|
pm2.61i | ⊢ 𝜓 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . 2 ⊢ (𝜑 → 𝜑) | |
2 | pm2.61i.2 | . . 3 ⊢ (¬ 𝜑 → 𝜓) | |
3 | pm2.61i.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
4 | 2, 3 | ja 173 | . 2 ⊢ ((𝜑 → 𝜑) → 𝜓) |
5 | 1, 4 | ax-mp 5 | 1 ⊢ 𝜓 |
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