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Mirrors > Home > MPE Home > Th. List > Mathboxes > eliuniin | Structured version Visualization version Unicode version |
Description: Indexed union of indexed intersections. (Contributed by Glauco Siliprandi, 26-Jun-2021.) |
Ref | Expression |
---|---|
eliuniin.1 |
Ref | Expression |
---|---|
eliuniin |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eliuniin.1 | . . . . 5 | |
2 | 1 | eleq2i 2693 | . . . 4 |
3 | eliun 4524 | . . . 4 | |
4 | 2, 3 | sylbb 209 | . . 3 |
5 | eliin 4525 | . . . . . 6 | |
6 | 5 | ibi 256 | . . . . 5 |
7 | 6 | a1i 11 | . . . 4 |
8 | 7 | reximdv 3016 | . . 3 |
9 | 4, 8 | mpd 15 | . 2 |
10 | simp2 1062 | . . . . . 6 | |
11 | eliin 4525 | . . . . . . 7 | |
12 | 11 | biimpar 502 | . . . . . 6 |
13 | rspe 3003 | . . . . . 6 | |
14 | 10, 12, 13 | 3imp3i2an 1278 | . . . . 5 |
15 | 14, 3 | sylibr 224 | . . . 4 |
16 | 15, 2 | sylibr 224 | . . 3 |
17 | 16 | rexlimdv3a 3033 | . 2 |
18 | 9, 17 | impbid2 216 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 w3a 1037 wceq 1483 wcel 1990 wral 2912 wrex 2913 ciun 4520 ciin 4521 |
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-v 3202 df-iun 4522 df-iin 4523 |
This theorem is referenced by: (None) |
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