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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 3379 |
. 2
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2 | inssdif0im 3514 |
. 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 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2175 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-v 2762 df-dif 3155 df-in 3159 df-ss 3166 df-nul 3447 |
This theorem is referenced by: ssdifin0 3528 difdifdirss 3531 fvsnun1 5755 fvsnun2 5756 phplem2 6909 unfiin 6982 xpfi 6986 sbthlem7 7022 sbthlemi8 7023 exmidfodomrlemim 7261 fihashssdif 10889 zfz1isolem1 10911 fsumlessfi 11603 fprodsplit1f 11777 setsfun 12653 setsfun0 12654 setsslid 12669 |
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