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Theorem 2uasbanhVD 28924
Description: The following User's Proof is a Virtual Deduction proof (see: wvd1 28561) completed automatically by a Metamath tools program invoking mmj2 and the Metamath Proof Assistant. 2uasbanh 28549 is 2uasbanhVD 28924 without virtual deductions and was automatically derived from 2uasbanhVD 28924. (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 28566 . . . . . . . 8
2 simpl 444 . . . . . . . 8
31, 2e1_ 28629 . . . . . . 7
4 simpr 448 . . . . . . . . 9
51, 4e1_ 28629 . . . . . . . 8
6 simpl 444 . . . . . . . 8
75, 6e1_ 28629 . . . . . . 7
8 pm3.2 435 . . . . . . 7
93, 7, 8e11 28690 . . . . . 6
109in1 28563 . . . . 5
1110eximi 1585 . . . 4
1211eximi 1585 . . 3
13 simpr 448 . . . . . . . 8
145, 13e1_ 28629 . . . . . . 7
15 pm3.2 435 . . . . . . 7
163, 14, 15e11 28690 . . . . . 6
1716in1 28563 . . . . 5
1817eximi 1585 . . . 4
1918eximi 1585 . . 3
2012, 19jca 519 . 2
21 2uasbanhVD.1 . . 3
2221biimpi 187 . . . . . . . . 9
2322dfvd1ir 28565 . . . . . . . 8
24 simpl 444 . . . . . . . 8
2523, 24e1_ 28629 . . . . . . 7
26 simpl 444 . . . . . . . . . . 11
27262eximi 1586 . . . . . . . . . 10
2825, 27e1_ 28629 . . . . . . . . 9
29 a9e2ndeq 28547 . . . . . . . . . 10
3029biimpri 198 . . . . . . . . 9
3128, 30e1_ 28629 . . . . . . . 8
32 2sb5nd 28548 . . . . . . . 8
3331, 32e1_ 28629 . . . . . . 7
34 bi2 190 . . . . . . . 8
3534com12 29 . . . . . . 7
3625, 33, 35e11 28690 . . . . . 6
37 simpr 448 . . . . . . . 8
3823, 37e1_ 28629 . . . . . . 7
39 2sb5nd 28548 . . . . . . . 8
4031, 39e1_ 28629 . . . . . . 7
41 bi2 190 . . . . . . . 8
4241com12 29 . . . . . . 7
4338, 40, 42e11 28690 . . . . . 6
44 sban 2143 . . . . . . . 8
4544sbbii 1665 . . . . . . 7
46 sban 2143 . . . . . . 7
4745, 46bitri 241 . . . . . 6
48 simplbi2comg 1382 . . . . . . 7
4948com13 76 . . . . . 6
5036, 43, 47, 49e110 28678 . . . . 5
51 2sb5nd 28548 . . . . . 6
5231, 51e1_ 28629 . . . . 5
53 bi1 179 . . . . . 6
5453com12 29 . . . . 5
5550, 52, 54e11 28690 . . . 4
5655in1 28563 . . 3
5721, 56sylbir 205 . 2
5820, 57impbii 181 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 177   wo 358   wa 359  wal 1549  wex 1550   wceq 1652  wsb 1658 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-ne 2600  df-v 2950  df-vd1 28562
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