Metamath Proof Explorer

Theorem nfdm

Description: Bound-variable hypothesis builder for domain. (Contributed by NM, 30-Jan-2004) (Revised by Mario Carneiro, 15-Oct-2016)

Ref Expression
Hypothesis nfrn.1 
|- F/_ x A
Assertion nfdm 
|- F/_ x dom A

Proof

Step Hyp Ref Expression
1 nfrn.1 
 |-  F/_ x A
2 df-dm 
 |-  dom A = { y | E. z y A z }
3 nfcv 
 |-  F/_ x y
4 nfcv 
 |-  F/_ x z
5 3 1 4 nfbr 
 |-  F/ x y A z
6 5 nfex 
 |-  F/ x E. z y A z
7 6 nfab 
 |-  F/_ x { y | E. z y A z }
8 2 7 nfcxfr 
 |-  F/_ x dom A