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Mirrors > Home > ILE Home > Th. List > inss2 | Unicode version |
Description: The intersection of two classes is a subset of one of them. Part of Exercise 12 of [TakeutiZaring] p. 18. (Contributed by NM, 27-Apr-1994.) |
Ref | Expression |
---|---|
inss2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | incom 3319 | . 2 | |
2 | inss1 3347 | . 2 | |
3 | 1, 2 | eqsstrri 3180 | 1 |
Colors of variables: wff set class |
Syntax hints: cin 3120 wss 3121 |
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-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-in 3127 df-ss 3134 |
This theorem is referenced by: difin0 3488 bnd2 4159 ordin 4370 relin2 4730 relres 4919 ssrnres 5053 cnvcnv 5063 funinsn 5247 funimaexg 5282 fnresin2 5313 ssimaex 5557 ffvresb 5659 ofrfval 6069 ofvalg 6070 ofrval 6071 off 6073 ofres 6075 ofco 6079 offres 6114 tpostpos 6243 smores3 6272 tfrlem5 6293 tfrexlem 6313 erinxp 6587 pmresg 6654 unfiin 6903 ltrelpi 7286 peano5nnnn 7854 peano5nni 8881 rexanuz 10952 structcnvcnv 12432 restsspw 12589 eltg4i 12849 ntrss2 12915 ntrin 12918 isopn3 12919 resttopon 12965 restuni2 12971 cnrest2r 13031 cnptopresti 13032 cnptoprest 13033 lmss 13040 metrest 13300 tgioo 13340 2sqlem8 13753 2sqlem9 13754 peano5set 13975 |
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