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| Mirrors > Home > MPE Home > Th. List > preq2 | Structured version Visualization version GIF version | ||
| Description: Equality theorem for unordered pairs. (Contributed by NM, 15-Jul-1993.) |
| Ref | Expression |
|---|---|
| preq2 | ⊢ (𝐴 = 𝐵 → {𝐶, 𝐴} = {𝐶, 𝐵}) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | preq1 4733 | . 2 ⊢ (𝐴 = 𝐵 → {𝐴, 𝐶} = {𝐵, 𝐶}) | |
| 2 | prcom 4732 | . 2 ⊢ {𝐶, 𝐴} = {𝐴, 𝐶} | |
| 3 | prcom 4732 | . 2 ⊢ {𝐶, 𝐵} = {𝐵, 𝐶} | |
| 4 | 1, 2, 3 | 3eqtr4g 2802 | 1 ⊢ (𝐴 = 𝐵 → {𝐶, 𝐴} = {𝐶, 𝐵}) |
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