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Theorem sbcex2 3381
Description: Move existential quantifier in and out of class substitution. (Contributed by NM, 21-May-2004.) (Revised by NM, 18-Aug-2018.)
Assertion
Ref Expression
sbcex2
Distinct variable groups:   ,   ,

Proof of Theorem sbcex2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbcex 3337 . 2
2 sbcex 3337 . . 3
32exlimiv 1722 . 2
4 dfsbcq2 3330 . . 3
5 dfsbcq2 3330 . . . 4
65exbidv 1714 . . 3
7 sbex 2207 . . 3
84, 6, 7vtoclbg 3168 . 2
91, 3, 8pm5.21nii 353 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  =wceq 1395  E.wex 1612  [wsb 1739  e.wcel 1818   cvv 3109  [.wsbc 3327
This theorem is referenced by:  sbcabel  3416  csbuni  4277  csbxp  5086  csbdm  5202  sbcfung  5616  sbcexf  30518  onfrALTlem5  33314  bnj89  33774  bnj985  34011
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111  df-sbc 3328
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