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Theorem sbcor 3372
Description: Distribution of class substitution over disjunction. (Contributed by NM, 31-Dec-2016.) (Revised by NM, 17-Aug-2018.)
Assertion
Ref Expression
sbcor

Proof of Theorem sbcor
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbcex 3337 . 2
2 sbcex 3337 . . 3
3 sbcex 3337 . . 3
42, 3jaoi 379 . 2
5 dfsbcq2 3330 . . 3
6 dfsbcq2 3330 . . . 4
7 dfsbcq2 3330 . . . 4
86, 7orbi12d 709 . . 3
9 sbor 2139 . . 3
105, 8, 9vtoclbg 3168 . 2
111, 4, 10pm5.21nii 353 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  \/wo 368  =wceq 1395  [wsb 1739  e.wcel 1818   cvv 3109  [.wsbc 3327
This theorem is referenced by:  sbcori  30511  sbc3or  33302
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-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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