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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexun 3625 |
. . . 4
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2 | eliun 4296 |
. . . . 5
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3 | eliun 4296 |
. . . . 5
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4 | 2, 3 | orbi12i 528 |
. . . 4
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5 | 1, 4 | bitr4i 260 |
. . 3
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6 | eliun 4296 |
. . 3
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7 | elun 3585 |
. . 3
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8 | 5, 6, 7 | 3bitr4i 285 |
. 2
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9 | 8 | eqriv 2458 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-ral 2753 df-rex 2754 df-v 3058 df-un 3420 df-iun 4293 |
This theorem is referenced by: iunsuc 5523 funiunfv 6177 iunfi 7887 kmlem11 8615 ackbij1lem9 8683 fsum2dlem 13879 fsumiun 13929 fprod2dlem 14082 prmreclem4 14911 fiuncmp 20467 ovolfiniun 22502 finiunmbl 22545 volfiniun 22548 voliunlem1 22551 uniioombllem4 22592 iunxdif3 28223 iuninc 28224 ofpreima2 28317 indval2 28884 esum2dlem 28961 sigaclfu2 28991 fiunelros 29044 measvuni 29084 cvmliftlem10 30065 mrsubvrs 30208 mblfinlem2 32022 dfrcl4 36312 iunrelexp0 36338 comptiunov2i 36342 corclrcl 36343 trclfvdecomr 36364 dfrtrcl4 36374 corcltrcl 36375 cotrclrcl 36378 fiiuncl 37443 iunp1 37444 sge0iunmptlemfi 38292 iunxprg 39043 |
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