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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 808 | . . . 4 | |
2 | elin 3300 | . . . . 5 | |
3 | elin 3300 | . . . . 5 | |
4 | 2, 3 | orbi12i 754 | . . . 4 |
5 | 1, 4 | bitr4i 186 | . . 3 |
6 | elun 3258 | . . . 4 | |
7 | 6 | anbi2i 453 | . . 3 |
8 | elun 3258 | . . 3 | |
9 | 5, 7, 8 | 3bitr4i 211 | . 2 |
10 | 9 | ineqri 3310 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wo 698 wceq 1342 wcel 2135 cun 3109 cin 3110 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-un 3115 df-in 3117 |
This theorem is referenced by: indir 3366 undisj2 3462 disjssun 3467 difdifdirss 3488 disjpr2 3634 diftpsn3 3708 resundi 4891 |
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