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Mirrors > Home > MPE Home > Th. List > dmiun | Structured version Visualization version Unicode version |
Description: The domain of an indexed union. (Contributed by Mario Carneiro, 26-Apr-2016.) |
Ref | Expression |
---|---|
dmiun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexcom4 3225 | . . . 4 | |
2 | vex 3203 | . . . . . 6 | |
3 | 2 | eldm2 5322 | . . . . 5 |
4 | 3 | rexbii 3041 | . . . 4 |
5 | eliun 4524 | . . . . 5 | |
6 | 5 | exbii 1774 | . . . 4 |
7 | 1, 4, 6 | 3bitr4ri 293 | . . 3 |
8 | 2 | eldm2 5322 | . . 3 |
9 | eliun 4524 | . . 3 | |
10 | 7, 8, 9 | 3bitr4i 292 | . 2 |
11 | 10 | eqriv 2619 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 wex 1704 wcel 1990 wrex 2913 cop 4183 ciun 4520 cdm 5114 |
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-3an 1039 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-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-dm 5124 |
This theorem is referenced by: dprd2d2 18443 esum2d 30155 iunrelexp0 37994 |
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