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Theorem nfre1 2537
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 2478 . 2  |-  ( E. x  e.  A  ph  <->  E. x ( x  e.  A  /\  ph )
)
2 nfe1 1507 . 2  |-  F/ x E. x ( x  e.  A  /\  ph )
31, 2nfxfr 1485 1  |-  F/ x E. x  e.  A  ph
Colors of variables: wff set class
Syntax hints:    /\ wa 104   F/wnf 1471   E.wex 1503    e. wcel 2164   E.wrex 2473
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
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-rex 2478
This theorem is referenced by:  r19.29an  2636  nfiu1  3942  fun11iun  5521  eusvobj2  5904  fodjuomnilemdc  7203  ismkvnex  7214  prarloclem3step  7556  prmuloc2  7627  ltexprlemm  7660  caucvgprprlemaddq  7768  caucvgsrlemgt1  7855  axpre-suploclemres  7961  supinfneg  9660  infsupneg  9661  lbzbi  9681  divalglemeunn  12062  divalglemeuneg  12064  bezoutlemmain  12135  bezout  12148  lss1d  13879  pw1nct  15493  isomninnlem  15520  trirec0  15534  ismkvnnlem  15542
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