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| Description: Deduction adding union to the right in a class equality. (Contributed by NM, 29-Mar-1998.) | 
| Ref | Expression | 
|---|---|
| uneq1d.1 | ⊢ (𝜑 → 𝐴 = 𝐵) | 
| Ref | Expression | 
|---|---|
| uneq1d | ⊢ (𝜑 → (𝐴 ∪ 𝐶) = (𝐵 ∪ 𝐶)) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | uneq1d.1 | . 2 ⊢ (𝜑 → 𝐴 = 𝐵) | |
| 2 | uneq1 4160 | . 2 ⊢ (𝐴 = 𝐵 → (𝐴 ∪ 𝐶) = (𝐵 ∪ 𝐶)) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝐴 ∪ 𝐶) = (𝐵 ∪ 𝐶)) | 
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