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Theorem ceqsexgv 2784
 Description: Elimination of an existential quantifier, using implicit substitution. (Contributed by NM, 29-Dec-1996.)
Hypothesis
Ref Expression
ceqsexgv.1
Assertion
Ref Expression
ceqsexgv
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem ceqsexgv
StepHypRef Expression
1 nfv 1491 . 2
2 ceqsexgv.1 . 2
31, 2ceqsexg 2783 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1314  wex 1451   wcel 1463 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2244  df-v 2659 This theorem is referenced by:  ceqsrexv  2785  clel3g  2789  elxp4  4984  elxp5  4985  dmfco  5443  fndmdif  5479  fndmin  5481  fmptco  5540  rexrnmpo  5840  brtpos2  6102  xpsnen  6668  prarloc  7259  metrest  12495
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