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| Mirrors > Home > MPE Home > Th. List > ord | Structured version Visualization version GIF version | ||
| Description: Deduce implication from disjunction. (Contributed by NM, 18-May-1994.) |
| Ref | Expression |
|---|---|
| ord.1 | ⊢ (𝜑 → (𝜓 ∨ 𝜒)) |
| Ref | Expression |
|---|---|
| ord | ⊢ (𝜑 → (¬ 𝜓 → 𝜒)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ord.1 | . 2 ⊢ (𝜑 → (𝜓 ∨ 𝜒)) | |
| 2 | df-or 849 | . 2 ⊢ ((𝜓 ∨ 𝜒) ↔ (¬ 𝜓 → 𝜒)) | |
| 3 | 1, 2 | sylib 218 | 1 ⊢ (𝜑 → (¬ 𝜓 → 𝜒)) |
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