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Mirrors > Home > NFE Home > Th. List > preq12bg | Unicode version |
Description: Closed form of preq12b 4127. (Contributed by Scott Fenton, 28-Mar-2014.) |
Ref | Expression |
---|---|
preq12bg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | preq1 3799 | . . . . . . 7 | |
2 | 1 | eqeq1d 2361 | . . . . . 6 |
3 | eqeq1 2359 | . . . . . . . 8 | |
4 | 3 | anbi1d 685 | . . . . . . 7 |
5 | eqeq1 2359 | . . . . . . . 8 | |
6 | 5 | anbi1d 685 | . . . . . . 7 |
7 | 4, 6 | orbi12d 690 | . . . . . 6 |
8 | 2, 7 | bibi12d 312 | . . . . 5 |
9 | 8 | imbi2d 307 | . . . 4 |
10 | preq2 3800 | . . . . . . 7 | |
11 | 10 | eqeq1d 2361 | . . . . . 6 |
12 | eqeq1 2359 | . . . . . . . 8 | |
13 | 12 | anbi2d 684 | . . . . . . 7 |
14 | eqeq1 2359 | . . . . . . . 8 | |
15 | 14 | anbi2d 684 | . . . . . . 7 |
16 | 13, 15 | orbi12d 690 | . . . . . 6 |
17 | 11, 16 | bibi12d 312 | . . . . 5 |
18 | 17 | imbi2d 307 | . . . 4 |
19 | preq1 3799 | . . . . . . 7 | |
20 | 19 | eqeq2d 2364 | . . . . . 6 |
21 | eqeq2 2362 | . . . . . . . 8 | |
22 | 21 | anbi1d 685 | . . . . . . 7 |
23 | eqeq2 2362 | . . . . . . . 8 | |
24 | 23 | anbi2d 684 | . . . . . . 7 |
25 | 22, 24 | orbi12d 690 | . . . . . 6 |
26 | 20, 25 | bibi12d 312 | . . . . 5 |
27 | 26 | imbi2d 307 | . . . 4 |
28 | preq2 3800 | . . . . . . 7 | |
29 | 28 | eqeq2d 2364 | . . . . . 6 |
30 | eqeq2 2362 | . . . . . . . 8 | |
31 | 30 | anbi2d 684 | . . . . . . 7 |
32 | eqeq2 2362 | . . . . . . . 8 | |
33 | 32 | anbi1d 685 | . . . . . . 7 |
34 | 31, 33 | orbi12d 690 | . . . . . 6 |
35 | vex 2862 | . . . . . . 7 | |
36 | vex 2862 | . . . . . . 7 | |
37 | vex 2862 | . . . . . . 7 | |
38 | vex 2862 | . . . . . . 7 | |
39 | 35, 36, 37, 38 | preq12b 4127 | . . . . . 6 |
40 | 29, 34, 39 | vtoclbg 2915 | . . . . 5 |
41 | 40 | a1i 10 | . . . 4 |
42 | 9, 18, 27, 41 | vtocl3ga 2924 | . . 3 |
43 | 42 | 3expa 1151 | . 2 |
44 | 43 | impr 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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