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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 |
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1 | inss1 3355 |
. 2
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2 | inssdif0im 3490 |
. 2
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3 | 1, 2 | ax-mp 5 |
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-in 3135 df-ss 3142 df-nul 3423 |
This theorem is referenced by: ssdifin0 3504 difdifdirss 3507 fvsnun1 5709 fvsnun2 5710 phplem2 6847 unfiin 6919 xpfi 6923 sbthlem7 6956 sbthlemi8 6957 exmidfodomrlemim 7194 fihashssdif 10782 zfz1isolem1 10804 fsumlessfi 11452 fprodsplit1f 11626 setsfun 12480 setsfun0 12481 setsslid 12495 |
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