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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 |
---|---|
disjdif |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inss1 3291 | . 2 | |
2 | inssdif0im 3425 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 cdif 3063 cin 3065 wss 3066 c0 3358 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-dif 3068 df-in 3072 df-ss 3079 df-nul 3359 |
This theorem is referenced by: ssdifin0 3439 difdifdirss 3442 fvsnun1 5610 fvsnun2 5611 phplem2 6740 unfiin 6807 xpfi 6811 sbthlem7 6844 sbthlemi8 6845 exmidfodomrlemim 7050 fihashssdif 10557 zfz1isolem1 10576 fsumlessfi 11222 setsfun 11983 setsfun0 11984 setsslid 11998 |
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