Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  sbcex2 Unicode version

Theorem sbcex2 2877
 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 2833 . 2
2 sbcex 2833 . . 3
32exlimiv 1530 . 2
4 dfsbcq2 2828 . . 3
5 dfsbcq2 2828 . . . 4
65exbidv 1748 . . 3
7 sbex 1923 . . 3
84, 6, 7vtoclbg 2669 . 2
91, 3, 8pm5.21nii 653 1
 Colors of variables: wff set class Syntax hints:   wb 103   wceq 1285  wex 1422   wcel 1434  wsb 1687  cvv 2611  wsbc 2825 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 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2613  df-sbc 2826 This theorem is referenced by:  csbdmg  4578
 Copyright terms: Public domain W3C validator