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| Mirrors > Home > MPE Home > Th. List > bicomi | Structured version Visualization version GIF version | ||
| Description: Inference from commutative law for logical equivalence. (Contributed by NM, 3-Jan-1993.) |
| Ref | Expression |
|---|---|
| bicomi.1 | ⊢ (𝜑 ↔ 𝜓) |
| Ref | Expression |
|---|---|
| bicomi | ⊢ (𝜓 ↔ 𝜑) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bicomi.1 | . 2 ⊢ (𝜑 ↔ 𝜓) | |
| 2 | bicom1 221 | . 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜓 ↔ 𝜑)) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝜓 ↔ 𝜑) |
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