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Theorem nfs1v 1919
Description:  x is not free in  [
y  /  x ] ph when  x and  y are distinct. (Contributed by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
nfs1v  |-  F/ x [ y  /  x ] ph
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)

Proof of Theorem nfs1v
StepHypRef Expression
1 hbs1 1918 . 2  |-  ( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph )
21nfi 1442 1  |-  F/ x [ y  /  x ] ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1440   [wsb 1742
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-11 1486  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514
This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743
This theorem is referenced by:  nfsbxy  1922  nfsbxyt  1923  sbco3v  1949  sbcomxyyz  1952  sbnf2  1961  mo2n  2034  mo23  2047  mor  2048  clelab  2283  cbvralf  2674  cbvrexf  2675  cbvralsv  2694  cbvrexsv  2695  cbvrab  2710  sbhypf  2761  mob2  2892  reu2  2900  sbcralt  3013  sbcrext  3014  sbcralg  3015  sbcreug  3017  sbcel12g  3046  sbceqg  3047  cbvreucsf  3095  cbvrabcsf  3096  disjiun  3962  cbvopab1  4039  cbvopab1s  4041  csbopabg  4044  cbvmptf  4060  cbvmpt  4061  opelopabsb  4222  frind  4314  tfis  4544  findes  4564  opeliunxp  4643  ralxpf  4734  rexxpf  4735  cbviota  5142  csbiotag  5165  isarep1  5258  cbvriota  5792  csbriotag  5794  abrexex2g  6070  abrexex2  6074  dfoprab4f  6143  finexdc  6849  ssfirab  6880  uzind4s  9506  zsupcllemstep  11844  bezoutlemmain  11897  cbvrald  13433  bj-bdfindes  13595  bj-findes  13627
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