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Theorem sbcexg 2933
 Description: Move existential quantifier in and out of class substitution. (Contributed by NM, 21-May-2004.)
Assertion
Ref Expression
sbcexg
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   ()   (,)

Proof of Theorem sbcexg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfsbcq2 2883 . 2
2 dfsbcq2 2883 . . 3
32exbidv 1779 . 2
4 sbex 1955 . 2
51, 3, 4vtoclbg 2719 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1314  wex 1451   wcel 1463  wsb 1718  wsbc 2880 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-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 2245  df-v 2660  df-sbc 2881 This theorem is referenced by:  sbcabel  2960  csbunig  3712  csbxpg  4588  csbrng  4968
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