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Theorem csbrngVD 37293
Description: Virtual deduction proof of csbrngOLD 37217. 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. csbrngOLD 37217 is csbrngVD 37293 without virtual deductions and was automatically derived from csbrngVD 37293.
 1:: 2:1: 3:1: 4:3: 5:2,4: 6:5: 7:6: 8:1: 9:7,8: 10:9: 11:10: 12:1: 13:11,12: 14:: 15:14: 16:1,15: 17:13,16: 18:: 19:17,18: qed:19:
(Contributed by Alan Sare, 10-Nov-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
csbrngVD

Proof of Theorem csbrngVD
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 idn1 36944 . . . . . . . . . . . 12
2 sbcel12gOLD 36905 . . . . . . . . . . . 12
31, 2e1a 37006 . . . . . . . . . . 11
4 csbconstg 3376 . . . . . . . . . . . . 13
51, 4e1a 37006 . . . . . . . . . . . 12
6 eleq1 2517 . . . . . . . . . . . 12
75, 6e1a 37006 . . . . . . . . . . 11
8 bibi1 329 . . . . . . . . . . . 12
98biimprd 227 . . . . . . . . . . 11
103, 7, 9e11 37067 . . . . . . . . . 10
1110gen11 36995 . . . . . . . . 9
12 exbi 1716 . . . . . . . . 9
1311, 12e1a 37006 . . . . . . . 8
14 sbcexgOLD 36904 . . . . . . . . . 10
1514bicomd 205 . . . . . . . . 9
161, 15e1a 37006 . . . . . . . 8
17 bitr3 36867 . . . . . . . . 9
1817com12 32 . . . . . . . 8
1913, 16, 18e11 37067 . . . . . . 7
2019gen11 36995 . . . . . 6
21 abbi 2565 . . . . . . 7
2221biimpi 198 . . . . . 6
2320, 22e1a 37006 . . . . 5
24 csbabgOLD 37211 . . . . . 6
251, 24e1a 37006 . . . . 5
26 eqeq2 2462 . . . . . 6
2726biimpd 211 . . . . 5
2823, 25, 27e11 37067 . . . 4
29 dfrn3 5024 . . . . . 6
3029ax-gen 1669 . . . . 5
31 csbeq2gOLD 36916 . . . . 5
321, 30, 31e10 37073 . . . 4
33 eqeq2 2462 . . . . 5
3433biimpd 211 . . . 4
3528, 32, 34e11 37067 . . 3
36 dfrn3 5024 . . 3
37 eqeq2 2462 . . . 4
3837biimprcd 229 . . 3
3935, 36, 38e10 37073 . 2
4039in1 36941 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188  wal 1442   wceq 1444  wex 1663   wcel 1887  cab 2437  wsbc 3267  csb 3363  cop 3974   crn 4835 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-9 1896  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431  ax-sep 4525  ax-nul 4534  ax-pr 4639 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 987  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-eu 2303  df-mo 2304  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ne 2624  df-rab 2746  df-v 3047  df-sbc 3268  df-csb 3364  df-dif 3407  df-un 3409  df-in 3411  df-ss 3418  df-nul 3732  df-if 3882  df-sn 3969  df-pr 3971  df-op 3975  df-br 4403  df-opab 4462  df-cnv 4842  df-dm 4844  df-rn 4845  df-vd1 36940 This theorem is referenced by: (None)
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