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Mirrors > Home > ILE Home > Th. List > difundi | Unicode version |
Description: Distributive law for class difference. Theorem 39 of [Suppes] p. 29. (Contributed by NM, 17-Aug-2004.) |
Ref | Expression |
---|---|
difundi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldif 3138 |
. . . 4
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2 | eldif 3138 |
. . . 4
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3 | 1, 2 | anbi12i 460 |
. . 3
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4 | elin 3318 |
. . 3
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5 | eldif 3138 |
. . . . . 6
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6 | elun 3276 |
. . . . . . . 8
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7 | 6 | notbii 668 |
. . . . . . 7
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8 | 7 | anbi2i 457 |
. . . . . 6
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9 | 5, 8 | bitri 184 |
. . . . 5
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10 | ioran 752 |
. . . . . 6
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11 | 10 | anbi2i 457 |
. . . . 5
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12 | 9, 11 | bitri 184 |
. . . 4
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13 | anandi 590 |
. . . 4
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14 | 12, 13 | bitri 184 |
. . 3
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15 | 3, 4, 14 | 3bitr4ri 213 |
. 2
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16 | 15 | eqriv 2174 |
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 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-dif 3131 df-un 3133 df-in 3135 |
This theorem is referenced by: undm 3393 undifdc 6922 uncld 13506 |
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