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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | andi 790 |
. . . 4
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2 | elin 3223 |
. . . . 5
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3 | elin 3223 |
. . . . 5
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4 | 2, 3 | orbi12i 736 |
. . . 4
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5 | 1, 4 | bitr4i 186 |
. . 3
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6 | elun 3181 |
. . . 4
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7 | 6 | anbi2i 450 |
. . 3
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8 | elun 3181 |
. . 3
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9 | 5, 7, 8 | 3bitr4i 211 |
. 2
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10 | 9 | ineqri 3233 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 |
This theorem depends on definitions: df-bi 116 df-tru 1315 df-nf 1418 df-sb 1717 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-v 2657 df-un 3039 df-in 3041 |
This theorem is referenced by: indir 3289 undisj2 3385 disjssun 3390 difdifdirss 3411 disjpr2 3551 diftpsn3 3625 resundi 4788 |
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