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Mirrors > Home > ILE Home > Th. List > intun | Unicode version |
Description: The class intersection of the union of two classes. Theorem 78 of [Suppes] p. 42. (Contributed by NM, 22-Sep-2002.) |
Ref | Expression |
---|---|
intun |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.26 1491 |
. . . 4
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2 | elun 3288 |
. . . . . . 7
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3 | 2 | imbi1i 238 |
. . . . . 6
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4 | jaob 711 |
. . . . . 6
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5 | 3, 4 | bitri 184 |
. . . . 5
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6 | 5 | albii 1480 |
. . . 4
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7 | vex 2752 |
. . . . . 6
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8 | 7 | elint 3862 |
. . . . 5
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9 | 7 | elint 3862 |
. . . . 5
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10 | 8, 9 | anbi12i 460 |
. . . 4
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11 | 1, 6, 10 | 3bitr4i 212 |
. . 3
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12 | 7 | elint 3862 |
. . 3
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13 | elin 3330 |
. . 3
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14 | 11, 12, 13 | 3bitr4i 212 |
. 2
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15 | 14 | eqriv 2184 |
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 df-int 3857 |
This theorem is referenced by: intunsn 3894 riinint 4900 |
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