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| Mirrors > Home > MPE Home > Th. List > eqcoms | Structured version Visualization version GIF version | ||
| Description: Inference applying commutative law for class equality to an antecedent. (Contributed by NM, 24-Jun-1993.) |
| Ref | Expression |
|---|---|
| eqcoms.1 | ⊢ (𝐴 = 𝐵 → 𝜑) |
| Ref | Expression |
|---|---|
| eqcoms | ⊢ (𝐵 = 𝐴 → 𝜑) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eqcom 2744 | . 2 ⊢ (𝐵 = 𝐴 ↔ 𝐴 = 𝐵) | |
| 2 | eqcoms.1 | . 2 ⊢ (𝐴 = 𝐵 → 𝜑) | |
| 3 | 1, 2 | sylbi 217 | 1 ⊢ (𝐵 = 𝐴 → 𝜑) |
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