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 
|- F/_ x A
Assertion nfcnv 
|- F/_ x `' A

Proof

Step Hyp Ref Expression
1 nfcnv.1 
 |-  F/_ x A
2 df-cnv 
 |-  `' A = { <. y , z >. | z A y }
3 nfcv 
 |-  F/_ x z
4 nfcv 
 |-  F/_ x y
5 3 1 4 nfbr 
 |-  F/ x z A y
6 5 nfopab 
 |-  F/_ x { <. y , z >. | z A y }
7 2 6 nfcxfr 
 |-  F/_ x `' A