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Mirrors > Home > MPE Home > Th. List > pm2.61dan | Structured version Visualization version GIF version |
Description: Elimination of an antecedent. (Contributed by NM, 1-Jan-2005.) |
Ref | Expression |
---|---|
pm2.61dan.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
pm2.61dan.2 | ⊢ ((𝜑 ∧ ¬ 𝜓) → 𝜒) |
Ref | Expression |
---|---|
pm2.61dan | ⊢ (𝜑 → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.61dan.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
2 | 1 | ex 416 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) |
3 | pm2.61dan.2 | . . 3 ⊢ ((𝜑 ∧ ¬ 𝜓) → 𝜒) | |
4 | 3 | ex 416 | . 2 ⊢ (𝜑 → (¬ 𝜓 → 𝜒)) |
5 | 2, 4 | pm2.61d 182 | 1 ⊢ (𝜑 → 𝜒) |
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