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Theorem nfs1v 1955
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 1954 . 2  |-  ( [ y  /  x ] ph  ->  A. x [ y  /  x ] ph )
21nfi 1473 1  |-  F/ x [ y  /  x ] ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1471   [wsb 1773
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774
This theorem is referenced by:  nfsbxy  1958  nfsbxyt  1959  sbco3v  1985  sbcomxyyz  1988  sbnf2  1997  mo2n  2070  mo23  2083  mor  2084  clelab  2319  cbvralf  2718  cbvrexf  2719  cbvralsv  2742  cbvrexsv  2743  cbvrab  2758  sbhypf  2809  mob2  2940  reu2  2948  sbcralt  3062  sbcrext  3063  sbcralg  3064  sbcreug  3066  sbcel12g  3095  sbceqg  3096  cbvreucsf  3145  cbvrabcsf  3146  disjiun  4024  cbvopab1  4102  cbvopab1s  4104  csbopabg  4107  cbvmptf  4123  cbvmpt  4124  opelopabsb  4290  frind  4383  tfis  4615  findes  4635  opeliunxp  4714  ralxpf  4808  rexxpf  4809  cbviota  5220  csbiotag  5247  isarep1  5340  cbvriota  5884  csbriotag  5886  abrexex2g  6172  abrexex2  6176  dfoprab4f  6246  finexdc  6958  ssfirab  6990  uzind4s  9655  zsupcllemstep  12082  bezoutlemmain  12135  nnwosdc  12176  cbvrald  15280  bj-bdfindes  15441  bj-findes  15473
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