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Mirrors > Home > MPE Home > Th. List > iunxun | Structured version Visualization version Unicode version |
Description: Separate a union in the index of an indexed union. (Contributed by NM, 26-Mar-2004.) (Proof shortened by Mario Carneiro, 17-Nov-2016.) |
Ref | Expression |
---|---|
iunxun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexun 3793 | . . . 4 | |
2 | eliun 4524 | . . . . 5 | |
3 | eliun 4524 | . . . . 5 | |
4 | 2, 3 | orbi12i 543 | . . . 4 |
5 | 1, 4 | bitr4i 267 | . . 3 |
6 | eliun 4524 | . . 3 | |
7 | elun 3753 | . . 3 | |
8 | 5, 6, 7 | 3bitr4i 292 | . 2 |
9 | 8 | eqriv 2619 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wo 383 wceq 1483 wcel 1990 wrex 2913 cun 3572 ciun 4520 |
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 |
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-ral 2917 df-rex 2918 df-v 3202 df-un 3579 df-iun 4522 |
This theorem is referenced by: iunxdif3 4606 iunxprg 4607 iunsuc 5807 funiunfv 6506 iunfi 8254 kmlem11 8982 ackbij1lem9 9050 fsum2dlem 14501 fsumiun 14553 fprod2dlem 14710 prmreclem4 15623 fiuncmp 21207 ovolfiniun 23269 finiunmbl 23312 volfiniun 23315 voliunlem1 23318 uniioombllem4 23354 iuninc 29379 ofpreima2 29466 indval2 30076 esum2dlem 30154 sigaclfu2 30184 fiunelros 30237 measvuni 30277 cvmliftlem10 31276 mrsubvrs 31419 mblfinlem2 33447 dfrcl4 37968 iunrelexp0 37994 comptiunov2i 37998 corclrcl 37999 trclfvdecomr 38020 dfrtrcl4 38030 corcltrcl 38031 cotrclrcl 38034 fiiuncl 39234 iunp1 39235 sge0iunmptlemfi 40630 ovolval4lem1 40863 |
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