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Theorem nfrn 4921
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 4700 . 2  |-  ran  A  =  dom  `' A
2 nfrn.1 . . . 4  |-  F/_ x A
32nfcnv 4860 . . 3  |-  F/_ x `' A
43nfdm 4920 . 2  |-  F/_ x dom  `' A
51, 4nfcxfr 2416 1  |-  F/_ x ran  A
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2406   `'ccnv 4688   dom cdm 4689   ran crn 4690
This theorem is referenced by:  nfima  5020  nff  5387  nffo  5450  zfrep6  5748  fliftfun  5811  ptbasfi  17276  itg2cnlem1  19116  dya2iocrrnval  23582  totbndbnd  26513  refsumcn  27701  stoweidlem27  27776  stoweidlem29  27778  stoweidlem31  27780  stoweidlem35  27784  stoweidlem59  27808  stoweidlem62  27811  stirlinglem5  27827  bnj1366  28862
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-cnv 4697  df-dm 4699  df-rn 4700
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