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Mirrors > Home > ILE Home > Th. List > dfdif3 | Unicode version |
Description: Alternate definition of class difference. Definition of relative set complement in Section 2.3 of [Pierik], p. 10. (Contributed by BJ and Jim Kingdon, 16-Jun-2022.) |
Ref | Expression |
---|---|
dfdif3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfdif2 3084 |
. 2
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2 | a9ev 1676 |
. . . . . . 7
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3 | 2 | biantrur 301 |
. . . . . 6
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4 | 19.41v 1875 |
. . . . . 6
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5 | 3, 4 | bitr4i 186 |
. . . . 5
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6 | sb56 1858 |
. . . . 5
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7 | equcom 1683 |
. . . . . . . 8
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8 | 7 | imbi1i 237 |
. . . . . . 7
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9 | eleq1w 2201 |
. . . . . . . . . 10
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10 | 9 | notbid 657 |
. . . . . . . . 9
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11 | 10 | pm5.74i 179 |
. . . . . . . 8
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12 | con2b 659 |
. . . . . . . 8
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13 | df-ne 2310 |
. . . . . . . . . 10
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14 | 13 | bicomi 131 |
. . . . . . . . 9
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15 | 14 | imbi2i 225 |
. . . . . . . 8
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16 | 11, 12, 15 | 3bitri 205 |
. . . . . . 7
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17 | 8, 16 | bitri 183 |
. . . . . 6
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18 | 17 | albii 1447 |
. . . . 5
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19 | 5, 6, 18 | 3bitri 205 |
. . . 4
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20 | df-ral 2422 |
. . . 4
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21 | 19, 20 | bitr4i 186 |
. . 3
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22 | 21 | rabbii 2675 |
. 2
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23 | 1, 22 | eqtri 2161 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-11 1485 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-ne 2310 df-ral 2422 df-rab 2426 df-dif 3078 |
This theorem is referenced by: (None) |
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