Definition df-members 36777

Description: Define the class of membership equivalence relations on their domain quotients. (Contributed by Peter Mazsa, 28-Nov-2022.) (Revised by Peter Mazsa, 24-Jul-2023.)

Assertion

Ref	Expression
df-members	⊢ MembErs = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) Ers 𝑎}

Detailed syntax breakdown of Definition df-members

Step	Hyp	Ref	Expression
1		cmembers 36360	. 2 class MembErs
2		cep 5494	. . . . . . 7 class E
3	2	ccnv 5588	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1538	. . . . . 6 class 𝑎
6	3, 5	cres 5591	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 36333	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		cers 36358	. . . 4 class Ers
9	7, 5, 8	wbr 5074	. . 3 wff ≀ (◡ E ↾ 𝑎) Ers 𝑎
10	9, 4	cab 2715	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) Ers 𝑎}
11	1, 10	wceq 1539	1 wff MembErs = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) Ers 𝑎}

This definition is referenced by: (None)