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| Description: Disjunction of three antecedents (inference). (Contributed by NM, 12-Sep-1995.) | 
| Ref | Expression | 
|---|---|
| 3jaoi.1 | ⊢ (𝜑 → 𝜓) | 
| 3jaoi.2 | ⊢ (𝜒 → 𝜓) | 
| 3jaoi.3 | ⊢ (𝜃 → 𝜓) | 
| Ref | Expression | 
|---|---|
| 3jaoi | ⊢ ((𝜑 ∨ 𝜒 ∨ 𝜃) → 𝜓) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | 3jaoi.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
| 2 | 3jaoi.2 | . . 3 ⊢ (𝜒 → 𝜓) | |
| 3 | 3jaoi.3 | . . 3 ⊢ (𝜃 → 𝜓) | |
| 4 | 1, 2, 3 | 3pm3.2i 1339 | . 2 ⊢ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜓) ∧ (𝜃 → 𝜓)) | 
| 5 | 3jao 1426 | . 2 ⊢ (((𝜑 → 𝜓) ∧ (𝜒 → 𝜓) ∧ (𝜃 → 𝜓)) → ((𝜑 ∨ 𝜒 ∨ 𝜃) → 𝜓)) | |
| 6 | 4, 5 | ax-mp 5 | 1 ⊢ ((𝜑 ∨ 𝜒 ∨ 𝜃) → 𝜓) | 
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