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Mirrors > Home > ILE Home > Th. List > uniuni | Unicode version |
Description: Expression for double union that moves union into a class builder. (Contributed by FL, 28-May-2007.) |
Ref | Expression |
---|---|
uniuni |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eluni 3792 | . . . . . 6 | |
2 | 1 | anbi2i 453 | . . . . 5 |
3 | 2 | exbii 1593 | . . . 4 |
4 | 19.42v 1894 | . . . . . . 7 | |
5 | 4 | bicomi 131 | . . . . . 6 |
6 | 5 | exbii 1593 | . . . . 5 |
7 | excom 1652 | . . . . . 6 | |
8 | anass 399 | . . . . . . . 8 | |
9 | ancom 264 | . . . . . . . 8 | |
10 | 8, 9 | bitr3i 185 | . . . . . . 7 |
11 | 10 | 2exbii 1594 | . . . . . 6 |
12 | exdistr 1897 | . . . . . 6 | |
13 | 7, 11, 12 | 3bitri 205 | . . . . 5 |
14 | eluni 3792 | . . . . . . . 8 | |
15 | 14 | bicomi 131 | . . . . . . 7 |
16 | 15 | anbi2i 453 | . . . . . 6 |
17 | 16 | exbii 1593 | . . . . 5 |
18 | 6, 13, 17 | 3bitri 205 | . . . 4 |
19 | vex 2729 | . . . . . . . . . . 11 | |
20 | 19 | uniex 4415 | . . . . . . . . . 10 |
21 | eleq2 2230 | . . . . . . . . . 10 | |
22 | 20, 21 | ceqsexv 2765 | . . . . . . . . 9 |
23 | exancom 1596 | . . . . . . . . 9 | |
24 | 22, 23 | bitr3i 185 | . . . . . . . 8 |
25 | 24 | anbi2i 453 | . . . . . . 7 |
26 | 19.42v 1894 | . . . . . . 7 | |
27 | ancom 264 | . . . . . . . . 9 | |
28 | anass 399 | . . . . . . . . 9 | |
29 | 27, 28 | bitri 183 | . . . . . . . 8 |
30 | 29 | exbii 1593 | . . . . . . 7 |
31 | 25, 26, 30 | 3bitr2i 207 | . . . . . 6 |
32 | 31 | exbii 1593 | . . . . 5 |
33 | excom 1652 | . . . . 5 | |
34 | exdistr 1897 | . . . . . 6 | |
35 | vex 2729 | . . . . . . . . . 10 | |
36 | eqeq1 2172 | . . . . . . . . . . . 12 | |
37 | 36 | anbi1d 461 | . . . . . . . . . . 11 |
38 | 37 | exbidv 1813 | . . . . . . . . . 10 |
39 | 35, 38 | elab 2870 | . . . . . . . . 9 |
40 | 39 | bicomi 131 | . . . . . . . 8 |
41 | 40 | anbi2i 453 | . . . . . . 7 |
42 | 41 | exbii 1593 | . . . . . 6 |
43 | 34, 42 | bitri 183 | . . . . 5 |
44 | 32, 33, 43 | 3bitri 205 | . . . 4 |
45 | 3, 18, 44 | 3bitri 205 | . . 3 |
46 | 45 | abbii 2282 | . 2 |
47 | df-uni 3790 | . 2 | |
48 | df-uni 3790 | . 2 | |
49 | 46, 47, 48 | 3eqtr4i 2196 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1343 wex 1480 wcel 2136 cab 2151 cuni 3789 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-bndl 1497 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-i5r 1523 ax-13 2138 ax-14 2139 ax-ext 2147 ax-sep 4100 ax-un 4411 |
This theorem depends on definitions: df-bi 116 df-tru 1346 df-nf 1449 df-sb 1751 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2297 df-rex 2450 df-v 2728 df-uni 3790 |
This theorem is referenced by: (None) |
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