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Theorem sbccomlem 2832
 Description: Lemma for sbccom 2833. (Contributed by NM, 14-Nov-2005.) (Revised by Mario Carneiro, 18-Oct-2016.)
Assertion
Ref Expression
sbccomlem
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem sbccomlem
StepHypRef Expression
1 excom 1554 . . . 4
2 exdistr 1787 . . . 4
3 an12 495 . . . . . . 7
43exbii 1496 . . . . . 6
5 19.42v 1786 . . . . . 6
64, 5bitri 173 . . . . 5
76exbii 1496 . . . 4
81, 2, 73bitr3i 199 . . 3
9 sbc5 2787 . . 3
10 sbc5 2787 . . 3
118, 9, 103bitr4i 201 . 2
12 sbc5 2787 . . 3
1312sbcbii 2818 . 2
14 sbc5 2787 . . 3
1514sbcbii 2818 . 2
1611, 13, 153bitr4i 201 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98   wceq 1243  wex 1381  wsbc 2764 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-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-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-sbc 2765 This theorem is referenced by:  sbccom  2833
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