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Mirrors > Home > ILE Home > Th. List > undi | Unicode version |
Description: Distributive law for union over intersection. Exercise 11 of [TakeutiZaring] p. 17. (Contributed by NM, 30-Sep-2002.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
undi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elin 3254 | . . . 4 | |
2 | 1 | orbi2i 751 | . . 3 |
3 | ordi 805 | . . 3 | |
4 | elin 3254 | . . . 4 | |
5 | elun 3212 | . . . . 5 | |
6 | elun 3212 | . . . . 5 | |
7 | 5, 6 | anbi12i 455 | . . . 4 |
8 | 4, 7 | bitr2i 184 | . . 3 |
9 | 2, 3, 8 | 3bitri 205 | . 2 |
10 | 9 | uneqri 3213 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wo 697 wceq 1331 wcel 1480 cun 3064 cin 3065 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-in 3072 |
This theorem is referenced by: undir 3321 undifdc 6805 |
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