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Mirrors > Home > ILE Home > Th. List > uniun | Unicode version |
Description: The class union of the union of two classes. Theorem 8.3 of [Quine] p. 53. (Contributed by NM, 20-Aug-1993.) |
Ref | Expression |
---|---|
uniun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.43 1621 | . . . 4 | |
2 | elun 3268 | . . . . . . 7 | |
3 | 2 | anbi2i 454 | . . . . . 6 |
4 | andi 813 | . . . . . 6 | |
5 | 3, 4 | bitri 183 | . . . . 5 |
6 | 5 | exbii 1598 | . . . 4 |
7 | eluni 3797 | . . . . 5 | |
8 | eluni 3797 | . . . . 5 | |
9 | 7, 8 | orbi12i 759 | . . . 4 |
10 | 1, 6, 9 | 3bitr4i 211 | . . 3 |
11 | eluni 3797 | . . 3 | |
12 | elun 3268 | . . 3 | |
13 | 10, 11, 12 | 3bitr4i 211 | . 2 |
14 | 13 | eqriv 2167 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wo 703 wceq 1348 wex 1485 wcel 2141 cun 3119 cuni 3794 |
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-v 2732 df-un 3125 df-uni 3795 |
This theorem is referenced by: unisuc 4396 unisucg 4397 |
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