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Theorem sbcssgVD 37280
Description: Virtual deduction proof of sbcssg 3880. The following User's Proof is a Virtual Deduction proof completed automatically by the tools program completeusersproof.cmd, which invokes Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. sbcssg 3880 is sbcssgVD 37280 without virtual deductions and was automatically derived from sbcssgVD 37280.
 1:: 2:1: 3:1: 4:2,3: 5:1: 6:4,5: 7:6: 8:7: 9:1: 10:8,9: 11:: 110:11: 12:1,110: 13:10,12: 14:: 15:13,14: qed:15:
(Contributed by Alan Sare, 22-Jul-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
sbcssgVD

Proof of Theorem sbcssgVD
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 idn1 36944 . . . . . . . . . 10
2 sbcel2gOLD 36906 . . . . . . . . . 10
31, 2e1a 37006 . . . . . . . . 9
4 sbcel2gOLD 36906 . . . . . . . . . 10
51, 4e1a 37006 . . . . . . . . 9
6 imbi12 324 . . . . . . . . 9
73, 5, 6e11 37067 . . . . . . . 8
8 sbcimg 3309 . . . . . . . . 9
91, 8e1a 37006 . . . . . . . 8
10 bibi1 329 . . . . . . . . 9
1110biimprcd 229 . . . . . . . 8
127, 9, 11e11 37067 . . . . . . 7
1312gen11 36995 . . . . . 6
14 albi 1690 . . . . . 6
1513, 14e1a 37006 . . . . 5
16 sbcalgOLD 36903 . . . . . 6
171, 16e1a 37006 . . . . 5
18 bibi1 329 . . . . . 6
1918biimprcd 229 . . . . 5
2015, 17, 19e11 37067 . . . 4
21 dfss2 3421 . . . . . 6
2221ax-gen 1669 . . . . 5
23 sbcbi 36900 . . . . 5
241, 22, 23e10 37073 . . . 4
25 bibi1 329 . . . . 5
2625biimprcd 229 . . . 4
2720, 24, 26e11 37067 . . 3
28 dfss2 3421 . . 3
29 biantr 942 . . . 4
3029ex 436 . . 3
3127, 28, 30e10 37073 . 2
3231in1 36941 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188  wal 1442   wcel 1887  wsbc 3267  csb 3363   wss 3404 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-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-v 3047  df-sbc 3268  df-csb 3364  df-in 3411  df-ss 3418  df-vd1 36940 This theorem is referenced by: (None)
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