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| Mirrors > Home > MPE Home > Th. List > opeq2d | Structured version Visualization version GIF version | ||
| Description: Equality deduction for ordered pairs. (Contributed by NM, 16-Dec-2006.) |
| Ref | Expression |
|---|---|
| opeq1d.1 | ⊢ (𝜑 → 𝐴 = 𝐵) |
| Ref | Expression |
|---|---|
| opeq2d | ⊢ (𝜑 → 〈𝐶, 𝐴〉 = 〈𝐶, 𝐵〉) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | opeq1d.1 | . 2 ⊢ (𝜑 → 𝐴 = 𝐵) | |
| 2 | opeq2 4874 | . 2 ⊢ (𝐴 = 𝐵 → 〈𝐶, 𝐴〉 = 〈𝐶, 𝐵〉) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 〈𝐶, 𝐴〉 = 〈𝐶, 𝐵〉) |
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