Metamath Proof Explorer


Theorem relbrcnvg

Description: When R is a relation, the sethood assumptions on brcnv can be omitted. (Contributed by Mario Carneiro, 28-Apr-2015)

Ref Expression
Assertion relbrcnvg RelRAR-1BBRA

Proof

Step Hyp Ref Expression
1 relcnv RelR-1
2 1 brrelex12i AR-1BAVBV
3 2 a1i RelRAR-1BAVBV
4 brrelex12 RelRBRABVAV
5 4 ancomd RelRBRAAVBV
6 5 ex RelRBRAAVBV
7 brcnvg AVBVAR-1BBRA
8 7 a1i RelRAVBVAR-1BBRA
9 3 6 8 pm5.21ndd RelRAR-1BBRA