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| Mirrors > Home > MPE Home > Th. List > orcd | Structured version Visualization version GIF version | ||
| Description: Deduction introducing a disjunct. A translation of natural deduction rule ∨ IR (∨ insertion right), see natded 30422. (Contributed by NM, 20-Sep-2007.) |
| Ref | Expression |
|---|---|
| orcd.1 | ⊢ (𝜑 → 𝜓) |
| Ref | Expression |
|---|---|
| orcd | ⊢ (𝜑 → (𝜓 ∨ 𝜒)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | orcd.1 | . 2 ⊢ (𝜑 → 𝜓) | |
| 2 | orc 868 | . 2 ⊢ (𝜓 → (𝜓 ∨ 𝜒)) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝜓 ∨ 𝜒)) |
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