Theorem eqabcri

Description: Equality of a class variable and a class abstraction (inference form). (Contributed by NM, 31-Jul-1994) (Proof shortened by Wolf Lammen, 15-Nov-2019)

	Ref	Expression
Hypothesis	eqabcri.1	|- { x | ph } = A
Assertion	eqabcri	|- ( ph <-> x e. A )

Proof

Step	Hyp	Ref	Expression
1		eqabcri.1	|- { x | ph } = A
2	1	eqcomi	|- A = { x | ph }
3	2	eqabri	|- ( x e. A <-> ph )
4	3	bicomi	|- ( ph <-> x e. A )