Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  sbcne12g Structured version   Unicode version

Theorem sbcne12g 3261
 Description: Distribute proper substitution through an inequality. (Contributed by Andrew Salmon, 18-Jun-2011.)
Assertion
Ref Expression
sbcne12g

Proof of Theorem sbcne12g
StepHypRef Expression
1 nne 2602 . . . . 5
21sbcbii 3208 . . . 4
32a1i 11 . . 3
4 sbcng 3193 . . 3
5 sbceqg 3259 . . . 4
6 nne 2602 . . . 4
75, 6syl6bbr 255 . . 3
83, 4, 73bitr3d 275 . 2
98con4bid 285 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wceq 1652   wcel 1725   wne 2598  wsbc 3153  csb 3243 This theorem is referenced by:  disjdsct  24082  cdlemkid3N  31667  cdlemkid4  31668 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-ne 2600  df-v 2950  df-sbc 3154  df-csb 3244
 Copyright terms: Public domain W3C validator