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Mirrors > Home > ILE Home > Th. List > indi | Unicode version |
Description: Distributive law for intersection over union. Exercise 10 of [TakeutiZaring] p. 17. (Contributed by NM, 30-Sep-2002.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
indi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | andi 807 | . . . 4 | |
2 | elin 3259 | . . . . 5 | |
3 | elin 3259 | . . . . 5 | |
4 | 2, 3 | orbi12i 753 | . . . 4 |
5 | 1, 4 | bitr4i 186 | . . 3 |
6 | elun 3217 | . . . 4 | |
7 | 6 | anbi2i 452 | . . 3 |
8 | elun 3217 | . . 3 | |
9 | 5, 7, 8 | 3bitr4i 211 | . 2 |
10 | 9 | ineqri 3269 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wo 697 wceq 1331 wcel 1480 cun 3069 cin 3070 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-in 3077 |
This theorem is referenced by: indir 3325 undisj2 3421 disjssun 3426 difdifdirss 3447 disjpr2 3587 diftpsn3 3661 resundi 4832 |
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