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Theorem sbcal 2875
 Description: Move universal quantifier in and out of class substitution. (Contributed by NM, 31-Dec-2016.)
Assertion
Ref Expression
sbcal
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem sbcal
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbcex 2833 . 2
2 sbcex 2833 . . 3
32sps 1471 . 2
4 dfsbcq2 2828 . . 3
5 dfsbcq2 2828 . . . 4
65albidv 1747 . . 3
7 sbal 1919 . . 3
84, 6, 7vtoclbg 2668 . 2
91, 3, 8pm5.21nii 653 1
 Colors of variables: wff set class Syntax hints:   wb 103  wal 1283   wceq 1285   wcel 1434  wsb 1687  cvv 2610  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 2612  df-sbc 2826 This theorem is referenced by:  sbcfung  4976
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