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| Mirrors > Home > MPE Home > Th. List > unieqd | Structured version Visualization version GIF version | ||
| Description: Deduction of equality of two class unions. (Contributed by NM, 21-Apr-1995.) |
| Ref | Expression |
|---|---|
| unieqd.1 | ⊢ (𝜑 → 𝐴 = 𝐵) |
| Ref | Expression |
|---|---|
| unieqd | ⊢ (𝜑 → ∪ 𝐴 = ∪ 𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | unieqd.1 | . 2 ⊢ (𝜑 → 𝐴 = 𝐵) | |
| 2 | unieq 4918 | . 2 ⊢ (𝐴 = 𝐵 → ∪ 𝐴 = ∪ 𝐵) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → ∪ 𝐴 = ∪ 𝐵) |
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