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Theorem nfrn 4607
Description: Bound-variable hypothesis builder for range. (Contributed by NM, 1-Sep-1999.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypothesis
Ref Expression
nfrn.1 𝑥𝐴
Assertion
Ref Expression
nfrn 𝑥ran 𝐴

Proof of Theorem nfrn
StepHypRef Expression
1 df-rn 4382 . 2 ran 𝐴 = dom 𝐴
2 nfrn.1 . . . 4 𝑥𝐴
32nfcnv 4542 . . 3 𝑥𝐴
43nfdm 4606 . 2 𝑥dom 𝐴
51, 4nfcxfr 2217 1 𝑥ran 𝐴
Colors of variables: wff set class
Syntax hints:  wnfc 2207  ccnv 4370  dom cdm 4371  ran crn 4372
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794  df-opab 3848  df-cnv 4379  df-dm 4381  df-rn 4382
This theorem is referenced by:  nfima  4706  nff  5074  nffo  5136  fliftfun  5467  nfiseq  9528
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