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Theorem sbcnel12g 3826
 Description: Distribute proper substitution through negated membership. (Contributed by Andrew Salmon, 18-Jun-2011.)
Assertion
Ref Expression
sbcnel12g

Proof of Theorem sbcnel12g
StepHypRef Expression
1 sbcng 3368 . 2
2 df-nel 2655 . . 3
32sbcbii 3387 . 2
4 df-nel 2655 . . 3
5 sbcel12 3823 . . 3
64, 5xchbinxr 311 . 2
71, 3, 63bitr4g 288 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  <->wb 184  e.wcel 1818  e/wnel 2653  [.wsbc 3327  [_csb 3434 This theorem is referenced by:  rusbcALT  31346 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-nel 2655  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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