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Mirrors > Home > ILE Home > Th. List > undif4 | Unicode version |
Description: Distribute union over difference. (Contributed by NM, 17-May-1998.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
undif4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.621 719 |
. . . . . . 7
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2 | olc 683 |
. . . . . . 7
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3 | 1, 2 | impbid1 141 |
. . . . . 6
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4 | 3 | anbi2d 457 |
. . . . 5
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5 | eldif 3044 |
. . . . . . 7
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6 | 5 | orbi2i 734 |
. . . . . 6
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7 | ordi 788 |
. . . . . 6
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8 | 6, 7 | bitri 183 |
. . . . 5
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9 | elun 3181 |
. . . . . 6
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10 | 9 | anbi1i 451 |
. . . . 5
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11 | 4, 8, 10 | 3bitr4g 222 |
. . . 4
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12 | elun 3181 |
. . . 4
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13 | eldif 3044 |
. . . 4
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14 | 11, 12, 13 | 3bitr4g 222 |
. . 3
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15 | 14 | alimi 1412 |
. 2
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16 | disj1 3377 |
. 2
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17 | dfcleq 2107 |
. 2
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18 | 15, 16, 17 | 3imtr4i 200 |
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 586 ax-in2 587 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 |
This theorem depends on definitions: df-bi 116 df-tru 1315 df-nf 1418 df-sb 1717 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-ral 2393 df-v 2657 df-dif 3037 df-un 3039 df-in 3041 df-nul 3328 |
This theorem is referenced by: phplem1 6697 |
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