Theorem rmorabex

Description: Restricted "at most one" existence implies a restricted class abstraction exists. (Contributed by NM, 17-Jun-2017)

	Ref	Expression
Assertion	rmorabex	|- ( E* x e. A ph -> { x e. A | ph } e. _V )

Proof

Step	Hyp	Ref	Expression
1		moabex	|- ( E* x ( x e. A /\ ph ) -> { x | ( x e. A /\ ph ) } e. _V )
2		df-rmo	|- ( E* x e. A ph <-> E* x ( x e. A /\ ph ) )
3		df-rab	|- { x e. A | ph } = { x | ( x e. A /\ ph ) }
4	3	eleq1i	|- ( { x e. A | ph } e. _V <-> { x | ( x e. A /\ ph ) } e. _V )
5	1 2 4	3imtr4i	|- ( E* x e. A ph -> { x e. A | ph } e. _V )