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| Mirrors > Home > MPE Home > Th. List > orbi12i | Structured version Visualization version GIF version | ||
| Description: Infer the disjunction of two equivalences. (Contributed by NM, 3-Jan-1993.) |
| Ref | Expression |
|---|---|
| orbi12i.1 | ⊢ (𝜑 ↔ 𝜓) |
| orbi12i.2 | ⊢ (𝜒 ↔ 𝜃) |
| Ref | Expression |
|---|---|
| orbi12i | ⊢ ((𝜑 ∨ 𝜒) ↔ (𝜓 ∨ 𝜃)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | orbi12i.2 | . . 3 ⊢ (𝜒 ↔ 𝜃) | |
| 2 | 1 | orbi2i 913 | . 2 ⊢ ((𝜑 ∨ 𝜒) ↔ (𝜑 ∨ 𝜃)) |
| 3 | orbi12i.1 | . . 3 ⊢ (𝜑 ↔ 𝜓) | |
| 4 | 3 | orbi1i 914 | . 2 ⊢ ((𝜑 ∨ 𝜃) ↔ (𝜓 ∨ 𝜃)) |
| 5 | 2, 4 | bitri 275 | 1 ⊢ ((𝜑 ∨ 𝜒) ↔ (𝜓 ∨ 𝜃)) |
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