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Theorem sbccsb2 3817
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 3307 . 2
2 elex 3090 . 2
3 abid 2441 . . . 4
43sbcbii 3357 . . 3
5 sbcel12 3789 . . . 4
6 csbvarg 3814 . . . . 5
76eleq1d 2523 . . . 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 1758  {cab 2439   cvv 3081  [.wsbc 3297  [_csb 3401
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-fal 1376  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-v 3083  df-sbc 3298  df-csb 3402  df-dif 3445  df-in 3449  df-ss 3456  df-nul 3752
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