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Theorem preq12bg 4128
Description: Closed form of preq12b 4127. (Contributed by Scott Fenton, 28-Mar-2014.)
Assertion
Ref Expression
preq12bg

Proof of Theorem preq12bg
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 preq1 3799 . . . . . . 7
21eqeq1d 2361 . . . . . 6
3 eqeq1 2359 . . . . . . . 8
43anbi1d 685 . . . . . . 7
5 eqeq1 2359 . . . . . . . 8
65anbi1d 685 . . . . . . 7
74, 6orbi12d 690 . . . . . 6
82, 7bibi12d 312 . . . . 5
98imbi2d 307 . . . 4
10 preq2 3800 . . . . . . 7
1110eqeq1d 2361 . . . . . 6
12 eqeq1 2359 . . . . . . . 8
1312anbi2d 684 . . . . . . 7
14 eqeq1 2359 . . . . . . . 8
1514anbi2d 684 . . . . . . 7
1613, 15orbi12d 690 . . . . . 6
1711, 16bibi12d 312 . . . . 5
1817imbi2d 307 . . . 4
19 preq1 3799 . . . . . . 7
2019eqeq2d 2364 . . . . . 6
21 eqeq2 2362 . . . . . . . 8
2221anbi1d 685 . . . . . . 7
23 eqeq2 2362 . . . . . . . 8
2423anbi2d 684 . . . . . . 7
2522, 24orbi12d 690 . . . . . 6
2620, 25bibi12d 312 . . . . 5
2726imbi2d 307 . . . 4
28 preq2 3800 . . . . . . 7
2928eqeq2d 2364 . . . . . 6
30 eqeq2 2362 . . . . . . . 8
3130anbi2d 684 . . . . . . 7
32 eqeq2 2362 . . . . . . . 8
3332anbi1d 685 . . . . . . 7
3431, 33orbi12d 690 . . . . . 6
35 vex 2862 . . . . . . 7
36 vex 2862 . . . . . . 7
37 vex 2862 . . . . . . 7
38 vex 2862 . . . . . . 7
3935, 36, 37, 38preq12b 4127 . . . . . 6
4029, 34, 39vtoclbg 2915 . . . . 5
4140a1i 10 . . . 4
429, 18, 27, 41vtocl3ga 2924 . . 3
43423expa 1151 . 2
4443impr 602 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176   wo 357   wa 358   w3a 934   wceq 1642   wcel 1710  cpr 3738
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-sn 3741  df-pr 3742
This theorem is referenced by: (None)
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