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Mirrors > Home > MPE Home > Th. List > imaiun | Structured version Visualization version Unicode version |
Description: The image of an indexed union is the indexed union of the images. (Contributed by Mario Carneiro, 18-Jun-2014.) |
Ref | Expression |
---|---|
imaiun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexcom4 3225 | . . . 4 | |
2 | vex 3203 | . . . . . 6 | |
3 | 2 | elima3 5473 | . . . . 5 |
4 | 3 | rexbii 3041 | . . . 4 |
5 | eliun 4524 | . . . . . . 7 | |
6 | 5 | anbi1i 731 | . . . . . 6 |
7 | r19.41v 3089 | . . . . . 6 | |
8 | 6, 7 | bitr4i 267 | . . . . 5 |
9 | 8 | exbii 1774 | . . . 4 |
10 | 1, 4, 9 | 3bitr4ri 293 | . . 3 |
11 | 2 | elima3 5473 | . . 3 |
12 | eliun 4524 | . . 3 | |
13 | 10, 11, 12 | 3bitr4i 292 | . 2 |
14 | 13 | eqriv 2619 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wa 384 wceq 1483 wex 1704 wcel 1990 wrex 2913 cop 4183 ciun 4520 cima 5117 |
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-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-iun 4522 df-br 4654 df-opab 4713 df-xp 5120 df-cnv 5122 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 |
This theorem is referenced by: imauni 6504 uniqs 7807 hsmexlem4 9251 hsmexlem5 9252 xkococnlem 21462 ismbf3d 23421 mbfimaopnlem 23422 i1fima 23445 i1fd 23448 itg1addlem5 23467 limciun 23658 sibfof 30402 eulerpartlemgh 30440 poimirlem30 33439 itg2addnclem2 33462 ftc1anclem6 33490 uniqsALTV 34101 smfresal 40995 |
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