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Mirrors > Home > ILE Home > Th. List > unssdif | Unicode version |
Description: Union of two classes and class difference. In classical logic this would be an equality. (Contributed by Jim Kingdon, 24-Jul-2018.) |
Ref | Expression |
---|---|
unssdif |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2644 |
. . . . . . . 8
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2 | eldif 3030 |
. . . . . . . 8
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3 | 1, 2 | mpbiran 892 |
. . . . . . 7
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4 | 3 | anbi1i 449 |
. . . . . 6
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5 | eldif 3030 |
. . . . . 6
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6 | ioran 710 |
. . . . . 6
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7 | 4, 5, 6 | 3bitr4i 211 |
. . . . 5
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8 | 7 | biimpi 119 |
. . . 4
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9 | 8 | con2i 597 |
. . 3
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10 | elun 3164 |
. . 3
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11 | eldif 3030 |
. . . 4
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12 | 1, 11 | mpbiran 892 |
. . 3
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13 | 9, 10, 12 | 3imtr4i 200 |
. 2
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14 | 13 | ssriv 3051 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 584 ax-in2 585 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 |
This theorem depends on definitions: df-bi 116 df-tru 1302 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-v 2643 df-dif 3023 df-un 3025 df-in 3027 df-ss 3034 |
This theorem is referenced by: (None) |
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