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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 2992 |
. 2
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2 | a9ev 1628 |
. . . . . . 7
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3 | 2 | biantrur 297 |
. . . . . 6
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4 | 19.41v 1825 |
. . . . . 6
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5 | 3, 4 | bitr4i 185 |
. . . . 5
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6 | sb56 1808 |
. . . . 5
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7 | equcom 1635 |
. . . . . . . 8
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8 | 7 | imbi1i 236 |
. . . . . . 7
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9 | eleq1w 2143 |
. . . . . . . . . 10
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10 | 9 | notbid 625 |
. . . . . . . . 9
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11 | 10 | pm5.74i 178 |
. . . . . . . 8
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12 | con2b 626 |
. . . . . . . 8
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13 | df-ne 2250 |
. . . . . . . . . 10
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14 | 13 | bicomi 130 |
. . . . . . . . 9
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15 | 14 | imbi2i 224 |
. . . . . . . 8
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16 | 11, 12, 15 | 3bitri 204 |
. . . . . . 7
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17 | 8, 16 | bitri 182 |
. . . . . 6
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18 | 17 | albii 1400 |
. . . . 5
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19 | 5, 6, 18 | 3bitri 204 |
. . . 4
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20 | df-ral 2358 |
. . . 4
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21 | 19, 20 | bitr4i 185 |
. . 3
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22 | 21 | rabbii 2598 |
. 2
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23 | 1, 22 | eqtri 2103 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 577 ax-in2 578 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-11 1438 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 |
This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-ne 2250 df-ral 2358 df-rab 2362 df-dif 2986 |
This theorem is referenced by: (None) |
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