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Theorem sbccomlem 3247
 Description: Lemma for sbccom 3248. (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 1759 . . . 4
2 exdistr 1933 . . . 4
3 an12 774 . . . . . . 7
43exbii 1593 . . . . . 6
5 19.42v 1932 . . . . . 6
64, 5bitri 242 . . . . 5
76exbii 1593 . . . 4
81, 2, 73bitr3i 268 . . 3
9 sbc5 3194 . . 3
10 sbc5 3194 . . 3
118, 9, 103bitr4i 270 . 2
12 sbc5 3194 . . 3
1312sbcbii 3228 . 2
14 sbc5 3194 . . 3
1514sbcbii 3228 . 2
1611, 13, 153bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360  wex 1551   wceq 1654  wsbc 3170 This theorem is referenced by:  sbccom  3248 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-v 2967  df-sbc 3171
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