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 _xA
Assertion nfdm _xdomA

Proof

Step Hyp Ref Expression
1 nfrn.1 _xA
2 df-dm domA=y|zyAz
3 nfcv _xy
4 nfcv _xz
5 3 1 4 nfbr xyAz
6 5 nfex xzyAz
7 6 nfab _xy|zyAz
8 2 7 nfcxfr _xdomA