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Theorem nfdm 4521
Description: Bound-variable hypothesis builder for domain. (Contributed by NM, 30-Jan-2004.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypothesis
Ref Expression
nfrn.1  F/_
Assertion
Ref Expression
nfdm  F/_ dom

Proof of Theorem nfdm
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-dm 4298 . 2  dom  {  |  }
2 nfcv 2175 . . . . 5  F/_
3 nfrn.1 . . . . 5  F/_
4 nfcv 2175 . . . . 5  F/_
52, 3, 4nfbr 3799 . . . 4  F/
65nfex 1525 . . 3  F/
76nfab 2179 . 2  F/_ {  |  }
81, 7nfcxfr 2172 1  F/_ dom
Colors of variables: wff set class
Syntax hints:  wex 1378   {cab 2023   F/_wnfc 2162   class class class wbr 3755   dom cdm 4288
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-dm 4298
This theorem is referenced by:  nfrn  4522  dmiin  4523  nffn  4938
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