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Theorem sbccomlem 3326
 Description: Lemma for sbccom 3327. (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 1944 . . . 4
2 exdistr 1843 . . . 4
3 an12 814 . . . . . . 7
43exbii 1726 . . . . . 6
5 19.42v 1842 . . . . . 6
64, 5bitri 257 . . . . 5
76exbii 1726 . . . 4
81, 2, 73bitr3i 283 . . 3
9 sbc5 3280 . . 3
10 sbc5 3280 . . 3
118, 9, 103bitr4i 285 . 2
12 sbc5 3280 . . 3
1312sbcbii 3311 . 2
14 sbc5 3280 . . 3
1514sbcbii 3311 . 2
1611, 13, 153bitr4i 285 1
 Colors of variables: wff setvar class Syntax hints:   wb 189   wa 376   wceq 1452  wex 1671  wsbc 3255 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-v 3033  df-sbc 3256 This theorem is referenced by:  sbccom  3327
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