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Theorem 2sb5ndVD 29022
Description: The following User's Proof is a Virtual Deduction proof (see: wvd1 28660) completed automatically by a Metamath tools program invoking mmj2 and the Metamath Proof Assistant. 2sb5nd 28647 is 2sb5ndVD 29022 without virtual deductions and was automatically derived from 2sb5ndVD 29022. (Contributed by Alan Sare, 30-Apr-2014.) (Proof modification is discouraged.) (New usage is discouraged.)
 1:: 2:1: 3:: 4:3: 5:4: 6:: 7:: 8:7: 9:6,8: 10:9: 11:5,10: 12:11: 13:: 14:: 15:14: 16:13,15: 17:16: 19:12,17: 20:19: 21:2,20: 22:21: 23:13: 24:22,23: 240:24: 241:: 242:241,240: 243:: 25:242,243: 26:: qed:25,26:
Assertion
Ref Expression
2sb5ndVD
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,,)

Proof of Theorem 2sb5ndVD
StepHypRef Expression
1 a9e2ndeq 28646 . 2
2 anabs5 785 . . . 4
3 2pm13.193 28639 . . . . . . . . 9
43exbii 1592 . . . . . . . 8
5 hbs1 2181 . . . . . . . . . . . . 13
6 idn1 28665 . . . . . . . . . . . . . 14
7 ax10o 2038 . . . . . . . . . . . . . 14
86, 7e1_ 28728 . . . . . . . . . . . . 13
9 imim1 72 . . . . . . . . . . . . 13
105, 8, 9e01 28792 . . . . . . . . . . . 12
1110in1 28662 . . . . . . . . . . 11
12 hbs1 2181 . . . . . . . . . . . . . . 15
1312sbt 2126 . . . . . . . . . . . . . 14
14 sbi1 2132 . . . . . . . . . . . . . 14
1513, 14e0_ 28884 . . . . . . . . . . . . 13
16 idn1 28665 . . . . . . . . . . . . . . 15
17 ax10 2025 . . . . . . . . . . . . . . . 16
1817con3i 129 . . . . . . . . . . . . . . 15
1916, 18e1_ 28728 . . . . . . . . . . . . . 14
20 sbal2 2211 . . . . . . . . . . . . . 14
2119, 20e1_ 28728 . . . . . . . . . . . . 13
22 imbi2 315 . . . . . . . . . . . . . 14
2322biimpcd 216 . . . . . . . . . . . . 13
2415, 21, 23e01 28792 . . . . . . . . . . . 12
2524in1 28662 . . . . . . . . . . 11
2611, 25pm2.61i 158 . . . . . . . . . 10
2726nfi 1560 . . . . . . . . 9
282719.41 1900 . . . . . . . 8
294, 28bitr3i 243 . . . . . . 7
3029exbii 1592 . . . . . 6
315nfi 1560 . . . . . . 7
323119.41 1900 . . . . . 6
3330, 32bitr2i 242 . . . . 5
3433anbi2i 676 . . . 4
352, 34bitr3i 243 . . 3
36 pm5.32 618 . . 3
3735, 36mpbir 201 . 2
381, 37sylbi 188 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   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 2417 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 2423  df-cleq 2429  df-clel 2432  df-ne 2601  df-v 2958  df-vd1 28661
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