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Theorem nfrn 4627
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  |-  F/_ x A
Assertion
Ref Expression
nfrn  |-  F/_ x ran  A

Proof of Theorem nfrn
StepHypRef Expression
1 df-rn 4402 . 2  |-  ran  A  =  dom  `' A
2 nfrn.1 . . . 4  |-  F/_ x A
32nfcnv 4562 . . 3  |-  F/_ x `' A
43nfdm 4626 . 2  |-  F/_ x dom  `' A
51, 4nfcxfr 2220 1  |-  F/_ x ran  A
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2210   `'ccnv 4390   dom cdm 4391   ran crn 4392
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 2065
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-un 2986  df-sn 3422  df-pr 3423  df-op 3425  df-br 3806  df-opab 3860  df-cnv 4399  df-dm 4401  df-rn 4402
This theorem is referenced by:  nfima  4726  nff  5094  nffo  5156  fliftfun  5487  nfiseq  9580
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