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| Mirrors > Home > MPE Home > Th. List > xpeq1d | Structured version Visualization version GIF version | ||
| Description: Equality deduction for Cartesian product. (Contributed by Jeff Madsen, 17-Jun-2010.) |
| Ref | Expression |
|---|---|
| xpeq1d.1 | ⊢ (𝜑 → 𝐴 = 𝐵) |
| Ref | Expression |
|---|---|
| xpeq1d | ⊢ (𝜑 → (𝐴 × 𝐶) = (𝐵 × 𝐶)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | xpeq1d.1 | . 2 ⊢ (𝜑 → 𝐴 = 𝐵) | |
| 2 | xpeq1 5699 | . 2 ⊢ (𝐴 = 𝐵 → (𝐴 × 𝐶) = (𝐵 × 𝐶)) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝐴 × 𝐶) = (𝐵 × 𝐶)) |
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