Theorem rabbieq

Description: Equivalent wff's correspond to restricted class abstractions which are equal with the same class. (Contributed by Peter Mazsa, 8-Jul-2019)

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

Proof

Step	Hyp	Ref	Expression
1		rabbieq.1	|- B = { x e. A | ph }
2		rabbieq.2	|- ( ph <-> ps )
3	2	rabbii	|- { x e. A | ph } = { x e. A | ps }
4	1 3	eqtri	|- B = { x e. A | ps }