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Theorem sbcor 3090
 Description: Distribution of class substitution over disjunction. (Contributed by NM, 31-Dec-2016.)
Assertion
Ref Expression
sbcor

Proof of Theorem sbcor
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbcex 3055 . 2
2 sbcex 3055 . . 3
3 sbcex 3055 . . 3
42, 3jaoi 368 . 2
5 dfsbcq2 3049 . . 3
6 dfsbcq2 3049 . . . 4
7 dfsbcq2 3049 . . . 4
86, 7orbi12d 690 . . 3
9 sbor 2066 . . 3
105, 8, 9vtoclbg 2915 . 2
111, 4, 10pm5.21nii 342 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wo 357   wceq 1642  wsb 1648   wcel 1710  cvv 2859  wsbc 3046 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-sbc 3047 This theorem is referenced by: (None)
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