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Theorem sbcex2 3202
 Description: Move existential quantifier in and out of class substitution. (Contributed by NM, 21-May-2004.)
Assertion
Ref Expression
sbcex2
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem sbcex2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbcex 3162 . 2
2 sbcex 3162 . . 3
32exlimiv 1644 . 2
4 dfsbcq2 3156 . . 3
5 dfsbcq2 3156 . . . 4
65exbidv 1636 . . 3
7 sbex 2204 . . 3
84, 6, 7vtoclbg 3004 . 2
91, 3, 8pm5.21nii 343 1
 Colors of variables: wff set class Syntax hints:   wb 177  wex 1550   wceq 1652  wsb 1658   wcel 1725  cvv 2948  wsbc 3153 This theorem is referenced by:  sbcfun  27954  bnj89  29023  bnj985  29261 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-sbc 3154
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