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Theorem nfrn 5400
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 5154 . 2 ran 𝐴 = dom 𝐴
2 nfrn.1 . . . 4 𝑥𝐴
32nfcnv 5333 . . 3 𝑥𝐴
43nfdm 5399 . 2 𝑥dom 𝐴
51, 4nfcxfr 2791 1 𝑥ran 𝐴
Colors of variables: wff setvar class
Syntax hints:  wnfc 2780  ccnv 5142  dom cdm 5143  ran crn 5144
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1056  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-rab 2950  df-v 3233  df-dif 3610  df-un 3612  df-in 3614  df-ss 3621  df-nul 3949  df-if 4120  df-sn 4211  df-pr 4213  df-op 4217  df-br 4686  df-opab 4746  df-cnv 5151  df-dm 5153  df-rn 5154
This theorem is referenced by:  nfima  5509  nff  6079  nffo  6152  fliftfun  6602  zfrep6  7176  ptbasfi  21432  utopsnneiplem  22098  restmetu  22422  itg2cnlem1  23573  acunirnmpt2  29588  acunirnmpt2f  29589  fsumiunle  29703  locfinreflem  30035  prodindf  30213  esumrnmpt2  30258  esumgect  30280  esum2d  30283  esumiun  30284  sigapildsys  30353  ldgenpisyslem1  30354  oms0  30487  breprexplema  30836  bnj1366  31026  totbndbnd  33718  refsumcn  39503  suprnmpt  39669  wessf1ornlem  39685  disjrnmpt2  39689  disjf1o  39692  disjinfi  39694  choicefi  39706  rnmptbd2lem  39777  infnsuprnmpt  39779  rnmptbdlem  39784  rnmptss2  39786  rnmptssbi  39791  supxrleubrnmpt  39945  suprleubrnmpt  39962  infrnmptle  39963  infxrunb3rnmpt  39968  uzub  39971  supminfrnmpt  39985  infxrgelbrnmpt  39996  infrpgernmpt  40008  supminfxrrnmpt  40014  limsupubuz  40263  liminflelimsuplem  40325  stoweidlem27  40562  stoweidlem29  40564  stoweidlem31  40566  stoweidlem35  40570  stoweidlem59  40594  stoweidlem62  40597  stirlinglem5  40613  fourierdlem31  40673  fourierdlem53  40694  fourierdlem80  40721  fourierdlem93  40734  sge00  40911  sge0f1o  40917  sge0gerp  40930  sge0pnffigt  40931  sge0lefi  40933  sge0ltfirp  40935  sge0resplit  40941  sge0reuz  40982  iunhoiioolem  41210  smfpimcc  41335  smfsup  41341  smfsupxr  41343  smfinf  41345  smflimsup  41355
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