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Theorem sbcnel12g 3260
 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 df-nel 2601 . . . 4
21sbcbii 3208 . . 3
32a1i 11 . 2
4 sbcng 3193 . 2
5 sbcel12g 3258 . . . 4
65notbid 286 . . 3
7 df-nel 2601 . . 3
86, 7syl6bbr 255 . 2
93, 4, 83bitrd 271 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wcel 1725   wnel 2599  wsbc 3153  csb 3243 This theorem is referenced by:  rusbcALT  27571 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-nel 2601  df-v 2950  df-sbc 3154  df-csb 3244
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