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Mirrors > Home > MPE Home > Th. List > base0 | Structured version Visualization version GIF version |
Description: The base set of the empty structure. (Contributed by David A. Wheeler, 7-Jul-2016.) |
Ref | Expression |
---|---|
base0 | ⊢ ∅ = (Base‘∅) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-base 16477 | . 2 ⊢ Base = Slot 1 | |
2 | 1 | str0 16523 | 1 ⊢ ∅ = (Base‘∅) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 ∅c0 4288 ‘cfv 6348 1c1 10526 Basecbs 16471 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 ax-sep 5194 ax-nul 5201 ax-pow 5257 ax-pr 5320 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-3an 1081 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-mo 2615 df-eu 2647 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-ral 3140 df-rex 3141 df-rab 3144 df-v 3494 df-sbc 3770 df-dif 3936 df-un 3938 df-in 3940 df-ss 3949 df-nul 4289 df-if 4464 df-sn 4558 df-pr 4560 df-op 4564 df-uni 4831 df-br 5058 df-opab 5120 df-mpt 5138 df-id 5453 df-xp 5554 df-rel 5555 df-cnv 5556 df-co 5557 df-dm 5558 df-iota 6307 df-fun 6350 df-fv 6356 df-slot 16475 df-base 16477 |
This theorem is referenced by: elbasfv 16532 elbasov 16533 ressbasss 16544 ress0 16546 0cat 16947 oppcbas 16976 fucbas 17218 xpcbas 17416 xpchomfval 17417 xpccofval 17420 0pos 17552 meet0 17735 join0 17736 oduclatb 17742 isipodrs 17759 0g0 17862 frmdplusg 18007 grpn0 18073 grpinvfvi 18084 mulgfvi 18168 symgbas 18436 symgplusg 18445 psgnfval 18557 subcmn 18886 invrfval 19352 00lss 19642 00lsp 19682 asclfval 20036 psrbas 20086 psrplusg 20089 psrmulr 20092 resspsrbas 20123 opsrle 20184 00ply1bas 20336 ply1basfvi 20337 ply1plusgfvi 20338 thlbas 20768 dsmmfi 20810 matbas0pc 20946 matbas0 20947 matrcl 20949 mdetfval 21123 madufval 21174 mdegfval 24583 uc1pval 24660 mon1pval 24662 dchrrcl 25743 vtxval0 26751 submomnd 30638 suborng 30815 bj-isrvec 34463 mendbas 39662 mendplusgfval 39663 mendmulrfval 39665 mendvscafval 39668 efmndbas 43970 efmndplusg 43978 |
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