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Theorem sbcne12gOLD 3828
 Description: Distribute proper substitution through an inequality. (Contributed by Andrew Salmon, 18-Jun-2011.) Obsolete as of 18-Aug-2018. Use sbcne12 3827 instead. (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
sbcne12gOLD

Proof of Theorem sbcne12gOLD
StepHypRef Expression
1 nne 2658 . . . . 5
21sbcbii 3387 . . . 4
32a1i 11 . . 3
4 sbcng 3368 . . 3
5 sbceqg 3825 . . . 4
6 nne 2658 . . . 4
75, 6syl6bbr 263 . . 3
83, 4, 73bitr3d 283 . 2
98con4bid 293 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  <->wb 184  =wceq 1395  e.wcel 1818  =/=wne 2652  [.wsbc 3327  [_csb 3434 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-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-sbc 3328  df-csb 3435
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