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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 15863 | . 2 ⊢ Base = Slot 1 | |
2 | 1 | str0 15911 | 1 ⊢ ∅ = (Base‘∅) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1483 ∅c0 3915 ‘cfv 5888 1c1 9937 Basecbs 15857 |
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-sep 4781 ax-nul 4789 ax-pow 4843 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-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-slot 15861 df-base 15863 |
This theorem is referenced by: elbasfv 15920 elbasov 15921 ressbasss 15932 ress0 15934 0cat 16349 oppcbas 16378 fucbas 16620 xpcbas 16818 xpchomfval 16819 xpccofval 16822 0pos 16954 meet0 17137 join0 17138 oduclatb 17144 isipodrs 17161 0g0 17263 frmdplusg 17391 grpn0 17454 grpinvfvi 17463 mulgfvi 17545 symgbas 17800 symgplusg 17809 psgnfval 17920 subcmn 18242 invrfval 18673 scaffval 18881 00lss 18942 00lsp 18981 asclfval 19334 psrbas 19378 psrplusg 19381 psrmulr 19384 resspsrbas 19415 opsrle 19475 00ply1bas 19610 ply1basfvi 19611 ply1plusgfvi 19612 thlbas 20040 dsmmbas2 20081 dsmmfi 20082 matbas0pc 20215 matbas0 20216 matrcl 20218 mdetfval 20392 madufval 20443 mdegfval 23822 uc1pval 23899 mon1pval 23901 dchrrcl 24965 vtxval0 25931 submomnd 29710 suborng 29815 mendbas 37754 mendplusgfval 37755 mendmulrfval 37757 mendvscafval 37760 |
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