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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 731 |
. . . 4
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2 | elin 3126 |
. . . . 5
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3 | elin 3126 |
. . . . 5
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4 | 2, 3 | orbi12i 681 |
. . . 4
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5 | 1, 4 | bitr4i 176 |
. . 3
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6 | elun 3084 |
. . . 4
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7 | 6 | anbi2i 430 |
. . 3
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8 | elun 3084 |
. . 3
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9 | 5, 7, 8 | 3bitr4i 201 |
. 2
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10 | 9 | ineqri 3130 |
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 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: indir 3186 undisj2 3280 disjssun 3285 difdifdirss 3307 disjpr2 3434 diftpsn3 3505 resundi 4625 |
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