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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 224 | . 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜓 ↔ 𝜑)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝜓 ↔ 𝜑) |
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