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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 | baseid 17190 | . 2 ⊢ Base = Slot (Base‘ndx) | |
2 | 1 | str0 17165 | 1 ⊢ ∅ = (Base‘∅) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 ∅c0 4326 ‘cfv 6553 ndxcnx 17169 Basecbs 17187 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2166 ax-ext 2699 ax-sep 5303 ax-nul 5310 ax-pow 5369 ax-pr 5433 ax-un 7746 ax-cnex 11202 ax-1cn 11204 ax-addcl 11206 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-3or 1085 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2529 df-eu 2558 df-clab 2706 df-cleq 2720 df-clel 2806 df-nfc 2881 df-ne 2938 df-ral 3059 df-rex 3068 df-reu 3375 df-rab 3431 df-v 3475 df-sbc 3779 df-csb 3895 df-dif 3952 df-un 3954 df-in 3956 df-ss 3966 df-pss 3968 df-nul 4327 df-if 4533 df-pw 4608 df-sn 4633 df-pr 4635 df-op 4639 df-uni 4913 df-iun 5002 df-br 5153 df-opab 5215 df-mpt 5236 df-tr 5270 df-id 5580 df-eprel 5586 df-po 5594 df-so 5595 df-fr 5637 df-we 5639 df-xp 5688 df-rel 5689 df-cnv 5690 df-co 5691 df-dm 5692 df-rn 5693 df-res 5694 df-ima 5695 df-pred 6310 df-ord 6377 df-on 6378 df-lim 6379 df-suc 6380 df-iota 6505 df-fun 6555 df-fn 6556 df-f 6557 df-f1 6558 df-fo 6559 df-f1o 6560 df-fv 6561 df-ov 7429 df-om 7877 df-2nd 8000 df-frecs 8293 df-wrecs 8324 df-recs 8398 df-rdg 8437 df-nn 12251 df-slot 17158 df-ndx 17170 df-base 17188 |
This theorem is referenced by: elbasfv 17193 elbasov 17194 ressbas 17222 ressbasssg 17224 ressbasssOLD 17227 ress0 17231 0cat 17676 oppcbas 17706 oppcbasOLD 17707 fucbas 17958 xpcbas 18176 xpchomfval 18177 xpccofval 18180 0pos 18320 0posOLD 18321 join0 18404 meet0 18405 oduclatb 18506 isipodrs 18536 0g0 18631 frmdplusg 18813 efmndbas 18830 efmndbasabf 18831 efmndplusg 18839 grpn0 18935 grpinvfvi 18946 mulgfvi 19036 psgnfval 19462 subcmn 19799 invrfval 20335 00lss 20832 00lsp 20872 thlbas 21635 thlbasOLD 21636 dsmmfi 21679 asclfval 21819 psrbas 21885 psrplusg 21888 psrmulr 21892 resspsrbas 21924 opsrle 21992 00ply1bas 22165 ply1basfvi 22166 ply1plusgfvi 22167 matbas0pc 22329 matbas0 22330 matrcl 22332 mdetfval 22508 madufval 22559 mdegfval 26018 uc1pval 26095 mon1pval 26097 dchrrcl 27193 vtxval0 28872 submomnd 32811 fracbas 33016 suborng 33054 mendbas 42639 mendplusgfval 42640 mendmulrfval 42642 mendvscafval 42645 ipolub00 48082 0thinc 48135 |
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