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Mirrors > Home > ILE Home > Th. List > intun | Unicode version |
Description: The class intersection of the union of two classes. Theorem 78 of [Suppes] p. 42. (Contributed by NM, 22-Sep-2002.) |
Ref | Expression |
---|---|
intun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.26 1474 | . . . 4 | |
2 | elun 3268 | . . . . . . 7 | |
3 | 2 | imbi1i 237 | . . . . . 6 |
4 | jaob 705 | . . . . . 6 | |
5 | 3, 4 | bitri 183 | . . . . 5 |
6 | 5 | albii 1463 | . . . 4 |
7 | vex 2733 | . . . . . 6 | |
8 | 7 | elint 3837 | . . . . 5 |
9 | 7 | elint 3837 | . . . . 5 |
10 | 8, 9 | anbi12i 457 | . . . 4 |
11 | 1, 6, 10 | 3bitr4i 211 | . . 3 |
12 | 7 | elint 3837 | . . 3 |
13 | elin 3310 | . . 3 | |
14 | 11, 12, 13 | 3bitr4i 211 | . 2 |
15 | 14 | eqriv 2167 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wo 703 wal 1346 wceq 1348 wcel 2141 cun 3119 cin 3120 cint 3831 |
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-in 3127 df-int 3832 |
This theorem is referenced by: intunsn 3869 riinint 4872 |
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