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Mirrors > Home > MPE Home > Th. List > pm2.61d | Structured version Visualization version GIF version |
Description: Deduction eliminating an antecedent. (Contributed by NM, 27-Apr-1994.) (Proof shortened by Wolf Lammen, 12-Sep-2013.) |
Ref | Expression |
---|---|
pm2.61d.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
pm2.61d.2 | ⊢ (𝜑 → (¬ 𝜓 → 𝜒)) |
Ref | Expression |
---|---|
pm2.61d | ⊢ (𝜑 → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.61d.2 | . . . 4 ⊢ (𝜑 → (¬ 𝜓 → 𝜒)) | |
2 | 1 | con1d 147 | . . 3 ⊢ (𝜑 → (¬ 𝜒 → 𝜓)) |
3 | pm2.61d.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
4 | 2, 3 | syld 47 | . 2 ⊢ (𝜑 → (¬ 𝜒 → 𝜒)) |
5 | 4 | pm2.18d 127 | 1 ⊢ (𝜑 → 𝜒) |
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