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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 1461 | . . . 4 | |
2 | elun 3248 | . . . . . . 7 | |
3 | 2 | imbi1i 237 | . . . . . 6 |
4 | jaob 700 | . . . . . 6 | |
5 | 3, 4 | bitri 183 | . . . . 5 |
6 | 5 | albii 1450 | . . . 4 |
7 | vex 2715 | . . . . . 6 | |
8 | 7 | elint 3813 | . . . . 5 |
9 | 7 | elint 3813 | . . . . 5 |
10 | 8, 9 | anbi12i 456 | . . . 4 |
11 | 1, 6, 10 | 3bitr4i 211 | . . 3 |
12 | 7 | elint 3813 | . . 3 |
13 | elin 3290 | . . 3 | |
14 | 11, 12, 13 | 3bitr4i 211 | . 2 |
15 | 14 | eqriv 2154 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wo 698 wal 1333 wceq 1335 wcel 2128 cun 3100 cin 3101 cint 3807 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-un 3106 df-in 3108 df-int 3808 |
This theorem is referenced by: intunsn 3845 riinint 4847 |
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