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Theorem nfex 1510
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 1393 . . 3 (φxφ)
32hbex 1509 . 2 (yφxyφ)
43nfi 1331 1 xyφ
Colors of variables: wff set class
Syntax hints:  wnf 1329  wex 1362
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 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-4 1381
This theorem depends on definitions:  df-bi 110  df-nf 1330
This theorem is referenced by:  eeor  1567  cbvex2  1779  eean  1788  nfeu1  1893  nfeuv  1900  nfel  2168  ceqsex2  2571  nfopab  3799  nfopab2  3801  cbvopab1  3804  cbvopab1s  3806  repizf2  3889  copsex2t  3956  copsex2g  3957  euotd  3965  mosubopt  4332  nfco  4428  dfdmf  4455  dfrnf  4502  nfdm  4505  fv3  5122  nfoprab2  5478  nfoprab3  5479  nfoprab  5480  cbvoprab1  5499  cbvoprab2  5500  cbvoprab3  5503
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