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Mirrors > Home > ILE Home > Th. List > disjdif | Unicode version |
Description: A class and its relative complement are disjoint. Theorem 38 of [Suppes] p. 29. (Contributed by NM, 24-Mar-1998.) |
Ref | Expression |
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disjdif |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inss1 3262 |
. 2
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2 | inssdif0im 3396 |
. 2
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3 | 1, 2 | ax-mp 7 |
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 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-v 2659 df-dif 3039 df-in 3043 df-ss 3050 df-nul 3330 |
This theorem is referenced by: ssdifin0 3410 difdifdirss 3413 fvsnun1 5571 fvsnun2 5572 phplem2 6700 unfiin 6767 xpfi 6771 sbthlem7 6803 sbthlemi8 6804 exmidfodomrlemim 7005 fihashssdif 10454 zfz1isolem1 10473 fsumlessfi 11118 setsfun 11834 setsfun0 11835 setsslid 11849 |
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