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Theorem sbc3orgVD 37247
Description: Virtual deduction proof of sbc3orgOLD 36893. The following user's proof is completed by invoking mmj2's unify command and using mmj2's StepSelector to pick all remaining steps of the Metamath proof.
 1:: 2:1,?: e1a 37006 3:: 32:3: 33:1,32,?: e10 37073 4:1,33,?: e11 37067 5:2,4,?: e11 37067 6:1,?: e1a 37006 7:6,?: e1a 37006 8:5,7,?: e11 37067 9:?: 10:8,9,?: e10 37073 qed:10:
(Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
sbc3orgVD

Proof of Theorem sbc3orgVD
StepHypRef Expression
1 idn1 36944 . . . . . 6
2 sbcorgOLD 36891 . . . . . 6
31, 2e1a 37006 . . . . 5
4 df-3or 986 . . . . . . . . 9
54bicomi 206 . . . . . . . 8
65ax-gen 1669 . . . . . . 7
7 spsbc 3280 . . . . . . 7
81, 6, 7e10 37073 . . . . . 6
9 sbcbig 3312 . . . . . . 7
109biimpd 211 . . . . . 6
111, 8, 10e11 37067 . . . . 5
12 bitr3 36867 . . . . . 6
1312com12 32 . . . . 5
143, 11, 13e11 37067 . . . 4
15 sbcorgOLD 36891 . . . . . 6
161, 15e1a 37006 . . . . 5
17 orbi1 712 . . . . 5
1816, 17e1a 37006 . . . 4
19 bibi1 329 . . . . 5
2019biimprd 227 . . . 4
2114, 18, 20e11 37067 . . 3
22 df-3or 986 . . . 4
2322bicomi 206 . . 3
24 bibi1 329 . . . 4
2524biimprd 227 . . 3
2621, 23, 25e10 37073 . 2
2726in1 36941 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wo 370   w3o 984  wal 1442   wcel 1887  wsbc 3267 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3or 986  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-v 3047  df-sbc 3268  df-vd1 36940 This theorem is referenced by: (None)
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