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Theorem csbingVD 37281
Description: Virtual deduction proof of csbingOLD 37215. 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. csbingOLD 37215 is csbingVD 37281 without virtual deductions and was automatically derived from csbingVD 37281.
 1:: 2:: 20:2: 30:1,20: 3:1,30: 4:1: 5:3,4: 6:1: 7:1: 8:6,7: 9:1: 10:9,8: 11:10: 12:11: 13:5,12: 14:: 15:13,14: qed:15:
(Contributed by Alan Sare, 22-Jul-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
csbingVD

Proof of Theorem csbingVD
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 idn1 36944 . . . . . 6
2 df-in 3411 . . . . . . . 8
32ax-gen 1669 . . . . . . 7
4 spsbc 3280 . . . . . . 7
51, 3, 4e10 37073 . . . . . 6
6 sbceqg 3773 . . . . . . 7
76biimpd 211 . . . . . 6
81, 5, 7e11 37067 . . . . 5
9 csbabgOLD 37211 . . . . . 6
101, 9e1a 37006 . . . . 5
11 eqeq1 2455 . . . . . 6
1211biimprd 227 . . . . 5
138, 10, 12e11 37067 . . . 4
14 sbcangOLD 36890 . . . . . . . 8
151, 14e1a 37006 . . . . . . 7
16 sbcel2gOLD 36906 . . . . . . . . 9
171, 16e1a 37006 . . . . . . . 8
18 sbcel2gOLD 36906 . . . . . . . . 9
191, 18e1a 37006 . . . . . . . 8
20 pm4.38 883 . . . . . . . . 9
2120ex 436 . . . . . . . 8
2217, 19, 21e11 37067 . . . . . . 7
23 bibi1 329 . . . . . . . 8
2423biimprd 227 . . . . . . 7
2515, 22, 24e11 37067 . . . . . 6
2625gen11 36995 . . . . 5
27 abbi 2565 . . . . . 6
2827biimpi 198 . . . . 5
2926, 28e1a 37006 . . . 4
30 eqeq1 2455 . . . . 5
3130biimprd 227 . . . 4
3213, 29, 31e11 37067 . . 3
33 df-in 3411 . . 3
34 eqeq2 2462 . . . 4
3534biimprcd 229 . . 3
3632, 33, 35e10 37073 . 2
3736in1 36941 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wa 371  wal 1442   wceq 1444   wcel 1887  cab 2437  wsbc 3267  csb 3363   cin 3403 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-vd1 36940 This theorem is referenced by: (None)
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