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Theorem sbccomlem 3116
 Description: Lemma for sbccom 3117. (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 1741 . . . 4
2 exdistr 1906 . . . 4
3 an12 772 . . . . . . 7
43exbii 1582 . . . . . 6
5 19.42v 1905 . . . . . 6
64, 5bitri 240 . . . . 5
76exbii 1582 . . . 4
81, 2, 73bitr3i 266 . . 3
9 sbc5 3070 . . 3
10 sbc5 3070 . . 3
118, 9, 103bitr4i 268 . 2
12 sbc5 3070 . . 3
1312sbcbii 3101 . 2
14 sbc5 3070 . . 3
1514sbcbii 3101 . 2
1611, 13, 153bitr4i 268 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358  wex 1541   wceq 1642  wsbc 3046 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-sbc 3047 This theorem is referenced by:  sbccom  3117
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