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Theorem rexsng 3442
 Description: Restricted existential quantification over a singleton. (Contributed by NM, 29-Jan-2012.)
Hypothesis
Ref Expression
ralsng.1
Assertion
Ref Expression
rexsng
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rexsng
StepHypRef Expression
1 rexsns 3440 . 2
2 ralsng.1 . . 3
32sbcieg 2847 . 2
41, 3syl5bb 190 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   wceq 1285   wcel 1434  wrex 2350  wsbc 2816  csn 3406 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-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rex 2355  df-v 2604  df-sbc 2817  df-sn 3412 This theorem is referenced by:  rexsn  3445  rexprg  3452  rextpg  3454  iunxsng  3761  imasng  4720
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