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| Mirrors > Home > MPE Home > Th. List > dmeqd | Structured version Visualization version GIF version | ||
| Description: Equality deduction for domain. (Contributed by NM, 4-Mar-2004.) |
| Ref | Expression |
|---|---|
| dmeqd.1 | ⊢ (𝜑 → 𝐴 = 𝐵) |
| Ref | Expression |
|---|---|
| dmeqd | ⊢ (𝜑 → dom 𝐴 = dom 𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | dmeqd.1 | . 2 ⊢ (𝜑 → 𝐴 = 𝐵) | |
| 2 | dmeq 5914 | . 2 ⊢ (𝐴 = 𝐵 → dom 𝐴 = dom 𝐵) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → dom 𝐴 = dom 𝐵) |
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