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Theorem nfrn 5187
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 4953 . 2  |-  ran  A  =  dom  `' A
2 nfrn.1 . . . 4  |-  F/_ x A
32nfcnv 5123 . . 3  |-  F/_ x `' A
43nfdm 5186 . 2  |-  F/_ x dom  `' A
51, 4nfcxfr 2562 1  |-  F/_ x ran  A
Colors of variables: wff setvar class
Syntax hints:   F/_wnfc 2550   `'ccnv 4941   dom cdm 4942   ran crn 4943
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-rab 2762  df-v 3060  df-dif 3416  df-un 3418  df-in 3420  df-ss 3427  df-nul 3738  df-if 3885  df-sn 3972  df-pr 3974  df-op 3978  df-br 4395  df-opab 4453  df-cnv 4950  df-dm 4952  df-rn 4953
This theorem is referenced by:  nfima  5286  nff  5666  nffo  5733  fliftfun  6149  zfrep6  6706  ptbasfi  20266  utopsnneiplem  20934  restmetu  21274  itg2cnlem1  22352  acunirnmpt2  27824  acunirnmpt2f  27825  locfinreflem  28176  esumrnmpt2  28395  esumgect  28417  esum2d  28420  esumiun  28421  sigapildsys  28490  ldgenpisyslem1  28491  oms0  28625  bnj1366  29096  totbndbnd  31548  refsumcn  36766  suprnmpt  36807  stoweidlem27  37159  stoweidlem29  37161  stoweidlem31  37163  stoweidlem35  37167  stoweidlem59  37191  stoweidlem62  37194  stirlinglem5  37210  fourierdlem31  37270  fourierdlem53  37292  fourierdlem80  37319  fourierdlem93  37332
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