Metamath Proof Explorer


Theorem nfcnv

Description: Bound-variable hypothesis builder for converse relation. (Contributed by NM, 31-Jan-2004) (Revised by Mario Carneiro, 15-Oct-2016)

Ref Expression
Hypothesis nfcnv.1 _ x A
Assertion nfcnv _ x A -1

Proof

Step Hyp Ref Expression
1 nfcnv.1 _ x A
2 df-cnv A -1 = y z | z A y
3 nfcv _ x z
4 nfcv _ x y
5 3 1 4 nfbr x z A y
6 5 nfopab _ x y z | z A y
7 2 6 nfcxfr _ x A -1