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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 819 |
. . . 4
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2 | elin 3330 |
. . . . 5
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3 | elin 3330 |
. . . . 5
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4 | 2, 3 | orbi12i 765 |
. . . 4
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5 | 1, 4 | bitr4i 187 |
. . 3
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6 | elun 3288 |
. . . 4
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7 | 6 | anbi2i 457 |
. . 3
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8 | elun 3288 |
. . 3
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9 | 5, 7, 8 | 3bitr4i 212 |
. 2
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10 | 9 | ineqri 3340 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-v 2751 df-un 3145 df-in 3147 |
This theorem is referenced by: indir 3396 undisj2 3493 disjssun 3498 difdifdirss 3519 disjpr2 3668 diftpsn3 3745 resundi 4932 |
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