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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 3126 | . . . 4 | |
2 | 1 | orbi2i 679 | . . 3 |
3 | ordi 729 | . . 3 | |
4 | elin 3126 | . . . 4 | |
5 | elun 3084 | . . . . 5 | |
6 | elun 3084 | . . . . 5 | |
7 | 5, 6 | anbi12i 433 | . . . 4 |
8 | 4, 7 | bitr2i 174 | . . 3 |
9 | 2, 3, 8 | 3bitri 195 | . 2 |
10 | 9 | uneqri 3085 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wo 629 wceq 1243 wcel 1393 cun 2915 cin 2916 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-in 2924 |
This theorem is referenced by: undir 3187 |
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