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Mirrors > Home > MPE Home > Th. List > dmeqi | Structured version Visualization version GIF version |
Description: Equality inference for domain. (Contributed by NM, 4-Mar-2004.) |
Ref | Expression |
---|---|
dmeqi.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
dmeqi | ⊢ dom 𝐴 = dom 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmeqi.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | dmeq 5746 | . 2 ⊢ (𝐴 = 𝐵 → dom 𝐴 = dom 𝐵) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ dom 𝐴 = dom 𝐵 |
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