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Theorem sbcnel12g 3773
 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 3307 . 2
2 df-nel 2624 . . 3
32sbcbii 3322 . 2
4 df-nel 2624 . . 3
5 sbcel12 3771 . . 3
64, 5xchbinxr 313 . 2
71, 3, 63bitr4g 292 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 188   wcel 1886   wnel 2622  wsbc 3266  csb 3362 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090  ax-ext 2430 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1446  df-fal 1449  df-ex 1663  df-nf 1667  df-sb 1797  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2580  df-nel 2624  df-v 3046  df-sbc 3267  df-csb 3363  df-dif 3406  df-in 3410  df-ss 3417  df-nul 3731 This theorem is referenced by:  rusbcALT  36784
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