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Mirrors > Home > MPE Home > Th. List > iunxiun | Structured version Visualization version Unicode version |
Description: Separate an indexed union in the index of an indexed union. (Contributed by Mario Carneiro, 5-Dec-2016.) |
Ref | Expression |
---|---|
iunxiun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eliun 4524 | . . . . . . . 8 | |
2 | 1 | anbi1i 731 | . . . . . . 7 |
3 | r19.41v 3089 | . . . . . . 7 | |
4 | 2, 3 | bitr4i 267 | . . . . . 6 |
5 | 4 | exbii 1774 | . . . . 5 |
6 | rexcom4 3225 | . . . . 5 | |
7 | 5, 6 | bitr4i 267 | . . . 4 |
8 | df-rex 2918 | . . . 4 | |
9 | eliun 4524 | . . . . . 6 | |
10 | df-rex 2918 | . . . . . 6 | |
11 | 9, 10 | bitri 264 | . . . . 5 |
12 | 11 | rexbii 3041 | . . . 4 |
13 | 7, 8, 12 | 3bitr4i 292 | . . 3 |
14 | eliun 4524 | . . 3 | |
15 | eliun 4524 | . . 3 | |
16 | 13, 14, 15 | 3bitr4i 292 | . 2 |
17 | 16 | eqriv 2619 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wa 384 wceq 1483 wex 1704 wcel 1990 wrex 2913 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-iun 4522 |
This theorem is referenced by: (None) |
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