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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 145 | . . 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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