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Theorem sbccomlem 2983
 Description: Lemma for sbccom 2984. (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 1642 . . . 4
2 exdistr 1881 . . . 4
3 an12 550 . . . . . . 7
43exbii 1584 . . . . . 6
5 19.42v 1878 . . . . . 6
64, 5bitri 183 . . . . 5
76exbii 1584 . . . 4
81, 2, 73bitr3i 209 . . 3
9 sbc5 2932 . . 3
10 sbc5 2932 . . 3
118, 9, 103bitr4i 211 . 2
12 sbc5 2932 . . 3
1312sbcbii 2968 . 2
14 sbc5 2932 . . 3
1514sbcbii 2968 . 2
1611, 13, 153bitr4i 211 1
 Colors of variables: wff set class Syntax hints:   wa 103   wb 104   wceq 1331  wex 1468  wsbc 2909 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-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-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-sbc 2910 This theorem is referenced by:  sbccom  2984
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