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| Mirrors > Home > MPE Home > Th. List > bitr4i | Structured version Visualization version GIF version | ||
| Description: An inference from transitive law for logical equivalence. (Contributed by NM, 3-Jan-1993.) |
| Ref | Expression |
|---|---|
| bitr4i.1 | ⊢ (𝜑 ↔ 𝜓) |
| bitr4i.2 | ⊢ (𝜒 ↔ 𝜓) |
| Ref | Expression |
|---|---|
| bitr4i | ⊢ (𝜑 ↔ 𝜒) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bitr4i.1 | . 2 ⊢ (𝜑 ↔ 𝜓) | |
| 2 | bitr4i.2 | . . 3 ⊢ (𝜒 ↔ 𝜓) | |
| 3 | 2 | bicomi 224 | . 2 ⊢ (𝜓 ↔ 𝜒) |
| 4 | 1, 3 | bitri 275 | 1 ⊢ (𝜑 ↔ 𝜒) |
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