Theorem brdmqssqs

Description: If A and R are sets, the domain quotient binary relation and the domain quotient predicate are the same. (Contributed by Peter Mazsa, 14-Aug-2021)

	Ref	Expression
Assertion	brdmqssqs	|- ( ( A e. V /\ R e. W ) -> ( R DomainQss A <-> R DomainQs A ) )

Proof

Step	Hyp	Ref	Expression
1		brdmqss	|- ( ( A e. V /\ R e. W ) -> ( R DomainQss A <-> ( dom R /. R ) = A ) )
2		df-dmqs	|- ( R DomainQs A <-> ( dom R /. R ) = A )
3	1 2	bitr4di	|- ( ( A e. V /\ R e. W ) -> ( R DomainQss A <-> R DomainQs A ) )