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| Mirrors > Home > MPE Home > Th. List > difeq2d | Structured version Visualization version GIF version | ||
| Description: Deduction adding difference to the left in a class equality. (Contributed by NM, 15-Nov-2002.) |
| Ref | Expression |
|---|---|
| difeq1d.1 | ⊢ (𝜑 → 𝐴 = 𝐵) |
| Ref | Expression |
|---|---|
| difeq2d | ⊢ (𝜑 → (𝐶 ∖ 𝐴) = (𝐶 ∖ 𝐵)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | difeq1d.1 | . 2 ⊢ (𝜑 → 𝐴 = 𝐵) | |
| 2 | difeq2 4120 | . 2 ⊢ (𝐴 = 𝐵 → (𝐶 ∖ 𝐴) = (𝐶 ∖ 𝐵)) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝐶 ∖ 𝐴) = (𝐶 ∖ 𝐵)) |
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