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Mirrors > Home > ILE Home > Th. List > iunxiun | 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 3877 | . . . . . . . 8 | |
2 | 1 | anbi1i 455 | . . . . . . 7 |
3 | r19.41v 2626 | . . . . . . 7 | |
4 | 2, 3 | bitr4i 186 | . . . . . 6 |
5 | 4 | exbii 1598 | . . . . 5 |
6 | rexcom4 2753 | . . . . 5 | |
7 | 5, 6 | bitr4i 186 | . . . 4 |
8 | df-rex 2454 | . . . 4 | |
9 | eliun 3877 | . . . . . 6 | |
10 | df-rex 2454 | . . . . . 6 | |
11 | 9, 10 | bitri 183 | . . . . 5 |
12 | 11 | rexbii 2477 | . . . 4 |
13 | 7, 8, 12 | 3bitr4i 211 | . . 3 |
14 | eliun 3877 | . . 3 | |
15 | eliun 3877 | . . 3 | |
16 | 13, 14, 15 | 3bitr4i 211 | . 2 |
17 | 16 | eqriv 2167 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1348 wex 1485 wcel 2141 wrex 2449 ciun 3873 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-iun 3875 |
This theorem is referenced by: (None) |
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