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Definition df-comembers 37530
Description: Define the class of comember equivalence relations on their domain quotients. (Contributed by Peter Mazsa, 28-Nov-2022.) (Revised by Peter Mazsa, 24-Jul-2023.)
Assertion
Ref Expression
df-comembers CoMembErs = {𝑎 ∣ ≀ ( E ↾ 𝑎) Ers 𝑎}

Detailed syntax breakdown of Definition df-comembers
StepHypRef Expression
1 ccomembers 37065 . 2 class CoMembErs
2 cep 5579 . . . . . . 7 class E
32ccnv 5675 . . . . . 6 class E
4 va . . . . . . 7 setvar 𝑎
54cv 1540 . . . . . 6 class 𝑎
63, 5cres 5678 . . . . 5 class ( E ↾ 𝑎)
76ccoss 37038 . . . 4 class ≀ ( E ↾ 𝑎)
8 cers 37063 . . . 4 class Ers
97, 5, 8wbr 5148 . . 3 wff ≀ ( E ↾ 𝑎) Ers 𝑎
109, 4cab 2709 . 2 class {𝑎 ∣ ≀ ( E ↾ 𝑎) Ers 𝑎}
111, 10wceq 1541 1 wff CoMembErs = {𝑎 ∣ ≀ ( E ↾ 𝑎) Ers 𝑎}
Colors of variables: wff setvar class
This definition is referenced by:  mpets  37707
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