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Mirrors > Home > MPE 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 1600 |
. . . 4
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2 | elun 3452 |
. . . . . . 7
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3 | 2 | imbi1i 316 |
. . . . . 6
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4 | jaob 759 |
. . . . . 6
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5 | 3, 4 | bitri 241 |
. . . . 5
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6 | 5 | albii 1572 |
. . . 4
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7 | vex 2923 |
. . . . . 6
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8 | 7 | elint 4020 |
. . . . 5
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9 | 7 | elint 4020 |
. . . . 5
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10 | 8, 9 | anbi12i 679 |
. . . 4
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11 | 1, 6, 10 | 3bitr4i 269 |
. . 3
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12 | 7 | elint 4020 |
. . 3
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13 | elin 3494 |
. . 3
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14 | 11, 12, 13 | 3bitr4i 269 |
. 2
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15 | 14 | eqriv 2405 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: intunsn 4053 riinint 5089 fiin 7389 elfiun 7397 elrfi 26642 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2389 |
This theorem depends on definitions: df-bi 178 df-or 360 df-an 361 df-tru 1325 df-ex 1548 df-nf 1551 df-sb 1656 df-clab 2395 df-cleq 2401 df-clel 2404 df-nfc 2533 df-v 2922 df-un 3289 df-in 3291 df-int 4015 |
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