Metamath Proof Explorer


Theorem cnvepresex

Description: Sethood condition for the restricted converse epsilon relation. (Contributed by Peter Mazsa, 24-Sep-2018)

Ref Expression
Assertion cnvepresex A V E -1 A V

Proof

Step Hyp Ref Expression
1 cnvepres E -1 A = x y | x A y x
2 id A V A V
3 abid2 y | y x = x
4 vex x V
5 3 4 eqeltri y | y x V
6 5 a1i A V x A y | y x V
7 2 6 opabex3d A V x y | x A y x V
8 1 7 eqeltrid A V E -1 A V