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Theorem sbccom2lem 28858
 Description: Lemma for sbccom2 28859. (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 sbc5 3208 . . . . . 6
21sbcbii 3243 . . . . 5
3 sbc5 3208 . . . . 5
42, 3bitri 249 . . . 4
5 19.42v 1928 . . . . . . 7
65bicomi 202 . . . . . 6
76exbii 1639 . . . . 5
8 excom 1792 . . . . 5
97, 8bitri 249 . . . 4
104, 9bitri 249 . . 3
11 sbc5 3208 . . . . 5
12 sbcan 3226 . . . . . 6
13 sbccom2lem.1 . . . . . . . 8
1413csbconstgi 28850 . . . . . . . 8
15 eqid 2441 . . . . . . . 8
1613, 14, 15sbceqi 28841 . . . . . . 7
1716anbi1i 690 . . . . . 6
1812, 17bitri 249 . . . . 5
1911, 18bitr3i 251 . . . 4
2019exbii 1639 . . 3
2110, 20bitri 249 . 2
22 sbc5 3208 . 2
2321, 22bitr4i 252 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 369   wceq 1364  wex 1591   wcel 1761  cvv 2970  wsbc 3183  csb 3285 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1713  ax-7 1733  ax-10 1780  ax-11 1785  ax-12 1797  ax-13 1948  ax-ext 2422 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1367  df-ex 1592  df-nf 1595  df-sb 1706  df-clab 2428  df-cleq 2434  df-clel 2437  df-nfc 2566  df-v 2972  df-sbc 3184  df-csb 3286 This theorem is referenced by:  sbccom2  28859
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