Theorem ruvALT

Description: Alternate proof of ruv with one fewer syntax step thanks to using elirrv instead of elirr . However, it does not change the compressed proof size or the number of symbols in the generated display, so it is not considered a shortening according to conventions . (Contributed by SN, 1-Sep-2024) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Assertion	ruvALT	|- { x | x e/ x } = _V

Proof

Step	Hyp	Ref	Expression
1		vex	|- x e. _V
2		elirrv	|- -. x e. x
3	2	nelir	|- x e/ x
4	1 3	2th	|- ( x e. _V <-> x e/ x )
5	4	abbi2i	|- _V = { x | x e/ x }
6	5	eqcomi	|- { x | x e/ x } = _V