Theorem rabeqel

Description: Class element of a restricted class abstraction. (Contributed by Peter Mazsa, 24-Jul-2021)

	Ref	Expression
Hypotheses	rabeqel.1	|- B = { x e. A | ph }
	rabeqel.2	|- ( x = C -> ( ph <-> ps ) )
Assertion	rabeqel	|- ( C e. B <-> ( ps /\ C e. A ) )

Proof

Step	Hyp	Ref	Expression
1		rabeqel.1	|- B = { x e. A | ph }
2		rabeqel.2	|- ( x = C -> ( ph <-> ps ) )
3	2 1	elrab2	|- ( C e. B <-> ( C e. A /\ ps ) )
4	3	biancomi	|- ( C e. B <-> ( ps /\ C e. A ) )