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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 3220 |
. 2
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2 | inssdif0im 3350 |
. 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 104 ax-ia2 105 ax-ia3 106 ax-in1 579 ax-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-v 2621 df-dif 3001 df-in 3005 df-ss 3012 df-nul 3287 |
This theorem is referenced by: ssdifin0 3364 difdifdirss 3367 fvsnun1 5494 fvsnun2 5495 phplem2 6567 unfiin 6634 xpfi 6638 sbthlem7 6670 sbthlemi8 6671 exmidfodomrlemim 6825 fihashssdif 10222 zfz1isolem1 10241 fsumlessfi 10850 setsfun 11524 setsfun0 11525 setsidn 11539 |
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