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Theorem sbcnel12g 3019
 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 2404 . . . 4
21sbcbii 2968 . . 3
32a1i 9 . 2
4 sbcng 2949 . 2
5 sbcel12g 3017 . . . 4
65notbid 656 . . 3
7 df-nel 2404 . . 3
86, 7syl6bbr 197 . 2
93, 4, 83bitrd 213 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 104   wcel 1480   wnel 2403  wsbc 2909  csb 3003 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-nel 2404  df-v 2688  df-sbc 2910  df-csb 3004 This theorem is referenced by: (None)
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