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Theorem nfex 1569
Description: If  x is not free in  ph, it is not free in  E. y ph. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof shortened by Wolf Lammen, 30-Dec-2017.)
Hypothesis
Ref Expression
nfex.1  |-  F/ x ph
Assertion
Ref Expression
nfex  |-  F/ x E. y ph

Proof of Theorem nfex
StepHypRef Expression
1 nfex.1 . . . 4  |-  F/ x ph
21nfri 1453 . . 3  |-  ( ph  ->  A. x ph )
32hbex 1568 . 2  |-  ( E. y ph  ->  A. x E. y ph )
43nfi 1392 1  |-  F/ x E. y ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1390   E.wex 1422
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by:  eeor  1626  cbvex2  1839  eean  1848  nfeu1  1953  nfeuv  1960  nfel  2228  ceqsex2  2640  nfopab  3854  nfopab2  3856  cbvopab1  3859  cbvopab1s  3861  repizf2  3944  copsex2t  4008  copsex2g  4009  euotd  4017  onintrab2im  4270  mosubopt  4431  nfco  4529  dfdmf  4556  dfrnf  4603  nfdm  4606  fv3  5229  nfoprab2  5586  nfoprab3  5587  nfoprab  5588  cbvoprab1  5607  cbvoprab2  5608  cbvoprab3  5611  cnvoprab  5886  ac6sfi  6431  nfsum1  10331  nfsum  10332
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