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Theorem sbccsb2 3851
Description: Substitution into a wff expressed in using substitution into a class. (Contributed by NM, 27-Nov-2005.) (Revised by NM, 18-Aug-2018.)
Assertion
Ref Expression
sbccsb2

Proof of Theorem sbccsb2
StepHypRef Expression
1 sbcex 3337 . 2
2 elex 3118 . 2
3 abid 2444 . . . 4
43sbcbii 3387 . . 3
5 sbcel12 3823 . . . 4
6 csbvarg 3848 . . . . 5
76eleq1d 2526 . . . 4
85, 7syl5bb 257 . . 3
94, 8syl5bbr 259 . 2
101, 2, 9pm5.21nii 353 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  e.wcel 1818  {cab 2442   cvv 3109  [.wsbc 3327  [_csb 3434
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-fal 1401  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785
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