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Mirrors > Home > NFE Home > Th. List > ninexg | Unicode version |
Description: The anti-intersection of two sets is a set. (Contributed by SF, 12-Jan-2015.) |
Ref | Expression |
---|---|
ninexg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nineq1 3235 |
. . 3
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2 | 1 | eleq1d 2419 |
. 2
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3 | nineq2 3236 |
. . 3
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4 | 3 | eleq1d 2419 |
. 2
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5 | ax-nin 4079 |
. . 3
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6 | isset 2864 |
. . . 4
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7 | dfcleq 2347 |
. . . . . 6
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8 | vex 2863 |
. . . . . . . . 9
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9 | 8 | elnin 3225 |
. . . . . . . 8
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10 | 9 | bibi2i 304 |
. . . . . . 7
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11 | 10 | albii 1566 |
. . . . . 6
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12 | 7, 11 | bitri 240 |
. . . . 5
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13 | 12 | exbii 1582 |
. . . 4
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14 | 6, 13 | bitri 240 |
. . 3
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15 | 5, 14 | mpbir 200 |
. 2
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16 | 2, 4, 15 | vtocl2g 2919 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4079 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-v 2862 df-nin 3212 |
This theorem is referenced by: ninex 4099 complexg 4100 inexg 4101 unexg 4102 |
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