Metamath Proof Explorer


Definition df-membparts

Description: Define the class of member partition relations on their domain quotients. (Contributed by Peter Mazsa, 26-Jun-2021)

Ref Expression
Assertion df-membparts MembParts = a | E -1 a Parts a

Detailed syntax breakdown

Step Hyp Ref Expression
0 cmembparts class MembParts
1 va setvar a
2 cep class E
3 2 ccnv class E -1
4 1 cv setvar a
5 3 4 cres class E -1 a
6 cparts class Parts
7 5 4 6 wbr wff E -1 a Parts a
8 7 1 cab class a | E -1 a Parts a
9 0 8 wceq wff MembParts = a | E -1 a Parts a