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Theorem 2uasbanhVD 37308
Description: The following User's Proof is a Virtual Deduction proof (see wvd1 36939) completed automatically by a Metamath tools program invoking mmj2 and the Metamath Proof Assistant. 2uasbanh 36928 is 2uasbanhVD 37308 without virtual deductions and was automatically derived from 2uasbanhVD 37308. (Contributed by Alan Sare, 31-May-2014.) (Proof modification is discouraged.) (New usage is discouraged.)
 h1:: 100:1: 2:100: 3:2: 4:3: 5:4: 6:5: 7:3,6: 8:2: 9:5: 10:8,9: 101:: 102:101: 103:: 104:102,103: 11:7,10,104: 110:5: 12:11,110: 120:12: 13:1,120: 14:: 15:14: 16:14: 17:16: 18:15,17: 19:18: 20:19: 21:20: 22:16: 23:15,22: 24:23: 25:24: 26:25: 27:21,26: qed:13,27:
Hypothesis
Ref Expression
2uasbanhVD.1
Assertion
Ref Expression
2uasbanhVD
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,,)   (,,,)   (,,,)

Proof of Theorem 2uasbanhVD
StepHypRef Expression
1 idn1 36944 . . . . . . . 8
2 simpl 459 . . . . . . . 8
31, 2e1a 37006 . . . . . . 7
4 simpr 463 . . . . . . . . 9
51, 4e1a 37006 . . . . . . . 8
6 simpl 459 . . . . . . . 8
75, 6e1a 37006 . . . . . . 7
8 pm3.2 449 . . . . . . 7
93, 7, 8e11 37067 . . . . . 6
109in1 36941 . . . . 5
1110eximi 1707 . . . 4
1211eximi 1707 . . 3
13 simpr 463 . . . . . . . 8
145, 13e1a 37006 . . . . . . 7
15 pm3.2 449 . . . . . . 7
163, 14, 15e11 37067 . . . . . 6
1716in1 36941 . . . . 5
1817eximi 1707 . . . 4
1918eximi 1707 . . 3
2012, 19jca 535 . 2
21 2uasbanhVD.1 . . 3
2221biimpi 198 . . . . . . . . 9
2322dfvd1ir 36943 . . . . . . . 8
24 simpl 459 . . . . . . . 8
2523, 24e1a 37006 . . . . . . 7
26 simpl 459 . . . . . . . . . . 11
27262eximi 1708 . . . . . . . . . 10
2825, 27e1a 37006 . . . . . . . . 9
29 ax6e2ndeq 36926 . . . . . . . . . 10
3029biimpri 210 . . . . . . . . 9
3128, 30e1a 37006 . . . . . . . 8
32 2sb5nd 36927 . . . . . . . 8
3331, 32e1a 37006 . . . . . . 7
34 biimpr 202 . . . . . . . 8
3534com12 32 . . . . . . 7
3625, 33, 35e11 37067 . . . . . 6
37 simpr 463 . . . . . . . 8
3823, 37e1a 37006 . . . . . . 7
39 2sb5nd 36927 . . . . . . . 8
4031, 39e1a 37006 . . . . . . 7
41 biimpr 202 . . . . . . . 8
4241com12 32 . . . . . . 7
4338, 40, 42e11 37067 . . . . . 6
44 sban 2228 . . . . . . . 8
4544sbbii 1804 . . . . . . 7
46 sban 2228 . . . . . . 7
4745, 46bitri 253 . . . . . 6
48 simplbi2comt 632 . . . . . . 7
4948com13 83 . . . . . 6
5036, 43, 47, 49e110 37055 . . . . 5
51 2sb5nd 36927 . . . . . 6
5231, 51e1a 37006 . . . . 5
53 biimp 197 . . . . . 6
5453com12 32 . . . . 5
5550, 52, 54e11 37067 . . . 4
5655in1 36941 . . 3
5721, 56sylbir 217 . 2
5820, 57impbii 191 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 188   wo 370   wa 371  wal 1442   wceq 1444  wex 1663  wsb 1797 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-ne 2624  df-v 3047  df-vd1 36940 This theorem is referenced by: (None)
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