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Theorem nfre1 2477
Description:  x is not free in  E. x  e.  A ph. (Contributed by NM, 19-Mar-1997.) (Revised by Mario Carneiro, 7-Oct-2016.)
Assertion
Ref Expression
nfre1  |-  F/ x E. x  e.  A  ph

Proof of Theorem nfre1
StepHypRef Expression
1 df-rex 2423 . 2  |-  ( E. x  e.  A  ph  <->  E. x ( x  e.  A  /\  ph )
)
2 nfe1 1473 . 2  |-  F/ x E. x ( x  e.  A  /\  ph )
31, 2nfxfr 1451 1  |-  F/ x E. x  e.  A  ph
Colors of variables: wff set class
Syntax hints:    /\ wa 103   F/wnf 1437   E.wex 1469    e. wcel 1481   E.wrex 2418
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 1424  ax-gen 1426  ax-ie1 1470
This theorem depends on definitions:  df-bi 116  df-nf 1438  df-rex 2423
This theorem is referenced by:  r19.29an  2575  nfiu1  3847  fun11iun  5392  eusvobj2  5764  fodjuomnilemdc  7020  ismkvnex  7033  prarloclem3step  7324  prmuloc2  7395  ltexprlemm  7428  caucvgprprlemaddq  7536  caucvgsrlemgt1  7623  axpre-suploclemres  7729  supinfneg  9413  infsupneg  9414  lbzbi  9431  divalglemeunn  11645  divalglemeuneg  11647  bezoutlemmain  11713  bezout  11726  pw1nct  13354  isomninnlem  13383  trirec0  13395  ismkvnnlem  13402
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