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Mirrors > Home > MPE Home > Th. List > uniuni | Structured version Visualization version 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 4439 | . . . . . 6 | |
2 | 1 | anbi2i 730 | . . . . 5 |
3 | 2 | exbii 1774 | . . . 4 |
4 | 19.42v 1918 | . . . . . . 7 | |
5 | 4 | bicomi 214 | . . . . . 6 |
6 | 5 | exbii 1774 | . . . . 5 |
7 | excom 2042 | . . . . . 6 | |
8 | anass 681 | . . . . . . . 8 | |
9 | ancom 466 | . . . . . . . 8 | |
10 | 8, 9 | bitr3i 266 | . . . . . . 7 |
11 | 10 | 2exbii 1775 | . . . . . 6 |
12 | exdistr 1919 | . . . . . 6 | |
13 | 7, 11, 12 | 3bitri 286 | . . . . 5 |
14 | eluni 4439 | . . . . . . . 8 | |
15 | 14 | bicomi 214 | . . . . . . 7 |
16 | 15 | anbi2i 730 | . . . . . 6 |
17 | 16 | exbii 1774 | . . . . 5 |
18 | 6, 13, 17 | 3bitri 286 | . . . 4 |
19 | vuniex 6954 | . . . . . . . . . 10 | |
20 | eleq2 2690 | . . . . . . . . . 10 | |
21 | 19, 20 | ceqsexv 3242 | . . . . . . . . 9 |
22 | exancom 1787 | . . . . . . . . 9 | |
23 | 21, 22 | bitr3i 266 | . . . . . . . 8 |
24 | 23 | anbi2i 730 | . . . . . . 7 |
25 | 19.42v 1918 | . . . . . . 7 | |
26 | ancom 466 | . . . . . . . . 9 | |
27 | anass 681 | . . . . . . . . 9 | |
28 | 26, 27 | bitri 264 | . . . . . . . 8 |
29 | 28 | exbii 1774 | . . . . . . 7 |
30 | 24, 25, 29 | 3bitr2i 288 | . . . . . 6 |
31 | 30 | exbii 1774 | . . . . 5 |
32 | excom 2042 | . . . . 5 | |
33 | exdistr 1919 | . . . . . 6 | |
34 | vex 3203 | . . . . . . . . . 10 | |
35 | eqeq1 2626 | . . . . . . . . . . . 12 | |
36 | 35 | anbi1d 741 | . . . . . . . . . . 11 |
37 | 36 | exbidv 1850 | . . . . . . . . . 10 |
38 | 34, 37 | elab 3350 | . . . . . . . . 9 |
39 | 38 | bicomi 214 | . . . . . . . 8 |
40 | 39 | anbi2i 730 | . . . . . . 7 |
41 | 40 | exbii 1774 | . . . . . 6 |
42 | 33, 41 | bitri 264 | . . . . 5 |
43 | 31, 32, 42 | 3bitri 286 | . . . 4 |
44 | 3, 18, 43 | 3bitri 286 | . . 3 |
45 | 44 | abbii 2739 | . 2 |
46 | df-uni 4437 | . 2 | |
47 | df-uni 4437 | . 2 | |
48 | 45, 46, 47 | 3eqtr4i 2654 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wa 384 wceq 1483 wex 1704 wcel 1990 cab 2608 cuni 4436 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-un 6949 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rex 2918 df-v 3202 df-uni 4437 |
This theorem is referenced by: (None) |
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