Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 3266 | . 2 | |
2 | inssdif0im 3400 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1316 cdif 3038 cin 3040 wss 3041 c0 3333 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-dif 3043 df-in 3047 df-ss 3054 df-nul 3334 |
This theorem is referenced by: ssdifin0 3414 difdifdirss 3417 fvsnun1 5585 fvsnun2 5586 phplem2 6715 unfiin 6782 xpfi 6786 sbthlem7 6819 sbthlemi8 6820 exmidfodomrlemim 7025 fihashssdif 10532 zfz1isolem1 10551 fsumlessfi 11197 setsfun 11921 setsfun0 11922 setsslid 11936 |
Copyright terms: Public domain | W3C validator |