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Theorem nfrn 5112
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 4889 . 2  |-  ran  A  =  dom  `' A
2 nfrn.1 . . . 4  |-  F/_ x A
32nfcnv 5051 . . 3  |-  F/_ x `' A
43nfdm 5111 . 2  |-  F/_ x dom  `' A
51, 4nfcxfr 2569 1  |-  F/_ x ran  A
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2559   `'ccnv 4877   dom cdm 4878   ran crn 4879
This theorem is referenced by:  nfima  5211  nff  5589  nffo  5652  zfrep6  5968  fliftfun  6034  ptbasfi  17613  utopsnneiplem  18277  restmetu  18617  itg2cnlem1  19653  totbndbnd  26498  refsumcn  27677  stoweidlem27  27752  stoweidlem29  27754  stoweidlem31  27756  stoweidlem35  27760  stoweidlem59  27784  stoweidlem62  27787  stirlinglem5  27803  bnj1366  29201
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-cnv 4886  df-dm 4888  df-rn 4889
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