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Mirrors > Home > MPE Home > Th. List > fovrnd | Structured version Visualization version Unicode version |
Description: An operation's value belongs to its codomain. (Contributed by Mario Carneiro, 29-Dec-2016.) |
Ref | Expression |
---|---|
fovrnd.1 | |
fovrnd.2 | |
fovrnd.3 |
Ref | Expression |
---|---|
fovrnd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fovrnd.1 | . 2 | |
2 | fovrnd.2 | . 2 | |
3 | fovrnd.3 | . 2 | |
4 | fovrn 6804 | . 2 | |
5 | 1, 2, 3, 4 | syl3anc 1326 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 cxp 5112 wf 5884 (class class class)co 6650 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-fv 5896 df-ov 6653 |
This theorem is referenced by: eroveu 7842 fseqenlem1 8847 rlimcn2 14321 homarel 16686 curf1cl 16868 curf2cl 16871 hofcllem 16898 yonedalem3b 16919 gasubg 17735 gacan 17738 gapm 17739 gastacos 17743 orbsta 17746 galactghm 17823 sylow1lem2 18014 sylow2alem2 18033 sylow3lem1 18042 efgcpbllemb 18168 frgpuplem 18185 frlmbas3 20115 mamucl 20207 mamuass 20208 mamudi 20209 mamudir 20210 mamuvs1 20211 mamuvs2 20212 mamulid 20247 mamurid 20248 mamutpos 20264 matgsumcl 20266 mavmulcl 20353 mavmulass 20355 mdetleib2 20394 mdetf 20401 mdetdiaglem 20404 mdetrlin 20408 mdetrsca 20409 mdetralt 20414 mdetunilem7 20424 maducoeval2 20446 madugsum 20449 madurid 20450 tsmsxplem2 21957 isxmet2d 22132 ismet2 22138 prdsxmetlem 22173 comet 22318 ipcn 23045 ovoliunlem2 23271 itg1addlem4 23466 itg1addlem5 23467 mbfi1fseqlem5 23486 limccnp2 23656 midcl 25669 pstmxmet 29940 cvmlift2lem9 31293 isbnd3 33583 prdsbnd 33592 iscringd 33797 rmxycomplete 37482 rmxyadd 37486 |
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