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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-dmqs | Structured version Visualization version GIF version |
Description: Define the domain quotient predicate. (Read: the domain quotient of 𝑅 is 𝐴.) If 𝐴 and 𝑅 are sets, the domain quotient binary relation and the domain quotient predicate are the same, see brdmqssqs 36739. (Contributed by Peter Mazsa, 9-Aug-2021.) |
Ref | Expression |
---|---|
df-dmqs | ⊢ (𝑅 DomainQs 𝐴 ↔ (dom 𝑅 / 𝑅) = 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class 𝐴 | |
2 | cR | . . 3 class 𝑅 | |
3 | 1, 2 | wdmqs 36336 | . 2 wff 𝑅 DomainQs 𝐴 |
4 | 2 | cdm 5588 | . . . 4 class dom 𝑅 |
5 | 4, 2 | cqs 8471 | . . 3 class (dom 𝑅 / 𝑅) |
6 | 5, 1 | wceq 1541 | . 2 wff (dom 𝑅 / 𝑅) = 𝐴 |
7 | 3, 6 | wb 205 | 1 wff (𝑅 DomainQs 𝐴 ↔ (dom 𝑅 / 𝑅) = 𝐴) |
Colors of variables: wff setvar class |
This definition is referenced by: brdmqssqs 36739 cnvepresdmqs 36744 dferALTV2 36759 |
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