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Theorem sbccom2lem 30497
 Description: Lemma for sbccom2 30498. (Contributed by Giovanni Mascellani, 31-May-2019.)
Hypothesis
Ref Expression
sbccom2lem.1
Assertion
Ref Expression
sbccom2lem
Distinct variable groups:   ,,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem sbccom2lem
StepHypRef Expression
1 sbcan 3354 . . . 4
2 sbc5 3336 . . . 4
3 sbccom2lem.1 . . . . . 6
43csbconstgi 30490 . . . . . 6
5 eqid 2441 . . . . . 6
63, 4, 5sbceqi 30481 . . . . 5
76anbi1i 695 . . . 4
81, 2, 73bitr3i 275 . . 3
98exbii 1652 . 2
10 sbc5 3336 . . . . 5
1110sbcbii 3371 . . . 4
12 sbc5 3336 . . . 4
1311, 12bitri 249 . . 3
14 19.42v 1759 . . . . . 6
1514bicomi 202 . . . . 5
1615exbii 1652 . . . 4
17 excom 1833 . . . 4
1816, 17bitri 249 . . 3
1913, 18bitri 249 . 2
20 sbc5 3336 . 2
219, 19, 203bitr4i 277 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 369   wceq 1381  wex 1597   wcel 1802  cvv 3093  wsbc 3311  csb 3417 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1603  ax-4 1616  ax-5 1689  ax-6 1732  ax-7 1774  ax-10 1821  ax-11 1826  ax-12 1838  ax-13 1983  ax-ext 2419 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1384  df-ex 1598  df-nf 1602  df-sb 1725  df-clab 2427  df-cleq 2433  df-clel 2436  df-nfc 2591  df-v 3095  df-sbc 3312  df-csb 3418 This theorem is referenced by:  sbccom2  30498
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