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Theorem nfex 1525
Description: If x is not free in φ, it is not free in yφ. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof shortened by Wolf Lammen, 30-Dec-2017.)
Hypothesis
Ref Expression
nfex.1 xφ
Assertion
Ref Expression
nfex xyφ

Proof of Theorem nfex
StepHypRef Expression
1 nfex.1 . . . 4 xφ
21nfri 1409 . . 3 (φxφ)
32hbex 1524 . 2 (yφxyφ)
43nfi 1348 1 xyφ
Colors of variables: wff set class
Syntax hints:  wnf 1346  wex 1378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  eeor  1582  cbvex2  1794  eean  1803  nfeu1  1908  nfeuv  1915  nfel  2183  ceqsex2  2588  nfopab  3816  nfopab2  3818  cbvopab1  3821  cbvopab1s  3823  repizf2  3906  copsex2t  3973  copsex2g  3974  euotd  3982  mosubopt  4348  nfco  4444  dfdmf  4471  dfrnf  4518  nfdm  4521  fv3  5140  nfoprab2  5497  nfoprab3  5498  nfoprab  5499  cbvoprab1  5518  cbvoprab2  5519  cbvoprab3  5522
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