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Theorem sbcne12g 2868
 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 sbceqg 2866 . . 3
21notbid 592 . 2
3 df-ne 2206 . . . . 5
43sbcbii 2818 . . . 4
5 sbcng 2803 . . . 4
64, 5syl5bb 181 . . 3
7 df-ne 2206 . . . 4
87a1i 9 . . 3
96, 8bibi12d 224 . 2
102, 9mpbird 156 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 98   wceq 1243   wcel 1393   wne 2204  wsbc 2764  csb 2852 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ne 2206  df-v 2559  df-sbc 2765  df-csb 2853 This theorem is referenced by: (None)
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