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| Mirrors > Home > MPE Home > Th. List > jaoi | Structured version Visualization version GIF version | ||
| Description: Inference disjoining the antecedents of two implications. (Contributed by NM, 5-Apr-1994.) |
| Ref | Expression |
|---|---|
| jaoi.1 | ⊢ (𝜑 → 𝜓) |
| jaoi.2 | ⊢ (𝜒 → 𝜓) |
| Ref | Expression |
|---|---|
| jaoi | ⊢ ((𝜑 ∨ 𝜒) → 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | pm2.53 852 | . . 3 ⊢ ((𝜑 ∨ 𝜒) → (¬ 𝜑 → 𝜒)) | |
| 2 | jaoi.2 | . . 3 ⊢ (𝜒 → 𝜓) | |
| 3 | 1, 2 | syl6 35 | . 2 ⊢ ((𝜑 ∨ 𝜒) → (¬ 𝜑 → 𝜓)) |
| 4 | jaoi.1 | . 2 ⊢ (𝜑 → 𝜓) | |
| 5 | 3, 4 | pm2.61d2 181 | 1 ⊢ ((𝜑 ∨ 𝜒) → 𝜓) |
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