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Mirrors > Home > MPE Home > Th. List > elfvex | Structured version Visualization version Unicode version |
Description: If a function value has a member, the argument is a set. (Contributed by Mario Carneiro, 6-Nov-2015.) |
Ref | Expression |
---|---|
elfvex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elfvdm 6220 | . 2 | |
2 | elex 3212 | . 2 | |
3 | 1, 2 | syl 17 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 cvv 3200 cdm 5114 cfv 5888 |
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-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-nul 4789 ax-pow 4843 |
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-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 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-dm 5124 df-iota 5851 df-fv 5896 |
This theorem is referenced by: elfvexd 6222 fviss 6256 fiin 8328 elharval 8468 elfzp12 12419 ismre 16250 ismri 16291 isacs 16312 oppccofval 16376 gexid 17996 efgrcl 18128 islss 18935 thlle 20041 islbs4 20171 istopon 20717 fgval 21674 fgcl 21682 ufilen 21734 ustssxp 22008 ustbasel 22010 ustincl 22011 ustdiag 22012 ustinvel 22013 ustexhalf 22014 ustfilxp 22016 ustbas2 22029 trust 22033 utopval 22036 elutop 22037 restutop 22041 ustuqtop5 22049 isucn 22082 psmetdmdm 22110 psmetf 22111 psmet0 22113 psmettri2 22114 psmetres2 22119 ismet2 22138 xmetpsmet 22153 metustfbas 22362 metust 22363 iscmet 23082 ulmscl 24133 1vgrex 25882 uvtxaisvtx 26289 vtxnbuvtx 26291 uvtxanbgrvtx 26293 uvtxnbgr 26301 wlkcompim 26527 clwlkcompim 26676 wwlkbp 26732 2wlkdlem7 26828 clwwlkbp 26883 3wlkdlem7 27026 metidval 29933 pstmval 29938 pstmxmet 29940 issiga 30174 insiga 30200 mvrsval 31402 mrsubcv 31407 mrsubccat 31415 mppsval 31469 topdifinffinlem 33195 istotbnd 33568 isbnd 33579 ismrc 37264 isnacs 37267 mzpcl1 37292 mzpcl2 37293 mzpf 37299 mzpadd 37301 mzpmul 37302 mzpsubmpt 37306 mzpnegmpt 37307 mzpexpmpt 37308 mzpindd 37309 mzpsubst 37311 mzpcompact2 37315 mzpcong 37539 sprel 41734 clintop 41844 assintop 41845 clintopcllaw 41847 assintopcllaw 41848 assintopass 41850 |
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