Theorem abex

Description: Conditions for a class abstraction to be a set. Remark: This proof is shorter than a proof using abexd . (Contributed by AV, 19-Apr-2025)

	Ref	Expression
Hypotheses	abex.1	|- ( ph -> x e. A )
	abex.2	|- A e. _V
Assertion	abex	|- { x | ph } e. _V

Proof

Step	Hyp	Ref	Expression
1		abex.1	|- ( ph -> x e. A )
2		abex.2	|- A e. _V
3		abss	|- ( { x | ph } C_ A <-> A. x ( ph -> x e. A ) )
4	3 1	mpgbir	|- { x | ph } C_ A
5	2 4	ssexi	|- { x | ph } e. _V