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| Mirrors > Home > MPE Home > Th. List > uneq1i | Structured version Visualization version GIF version | ||
| Description: Inference adding union to the right in a class equality. (Contributed by NM, 30-Aug-1993.) |
| Ref | Expression |
|---|---|
| uneq1i.1 | ⊢ 𝐴 = 𝐵 |
| Ref | Expression |
|---|---|
| uneq1i | ⊢ (𝐴 ∪ 𝐶) = (𝐵 ∪ 𝐶) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | uneq1i.1 | . 2 ⊢ 𝐴 = 𝐵 | |
| 2 | uneq1 4161 | . 2 ⊢ (𝐴 = 𝐵 → (𝐴 ∪ 𝐶) = (𝐵 ∪ 𝐶)) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝐴 ∪ 𝐶) = (𝐵 ∪ 𝐶) |
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