![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > baseid | Structured version Visualization version GIF version |
Description: Utility theorem: index-independent form of df-base 16481. (Contributed by NM, 20-Oct-2012.) |
Ref | Expression |
---|---|
baseid | ⊢ Base = Slot (Base‘ndx) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-base 16481 | . 2 ⊢ Base = Slot 1 | |
2 | 1nn 11636 | . 2 ⊢ 1 ∈ ℕ | |
3 | 1, 2 | ndxid 16501 | 1 ⊢ Base = Slot (Base‘ndx) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1538 ‘cfv 6324 1c1 10527 ndxcnx 16472 Slot cslot 16474 Basecbs 16475 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-10 2142 ax-11 2158 ax-12 2175 ax-ext 2770 ax-sep 5167 ax-nul 5174 ax-pow 5231 ax-pr 5295 ax-un 7441 ax-cnex 10582 ax-1cn 10584 ax-addcl 10586 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-3or 1085 df-3an 1086 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2070 df-mo 2598 df-eu 2629 df-clab 2777 df-cleq 2791 df-clel 2870 df-nfc 2938 df-ne 2988 df-ral 3111 df-rex 3112 df-reu 3113 df-rab 3115 df-v 3443 df-sbc 3721 df-csb 3829 df-dif 3884 df-un 3886 df-in 3888 df-ss 3898 df-pss 3900 df-nul 4244 df-if 4426 df-pw 4499 df-sn 4526 df-pr 4528 df-tp 4530 df-op 4532 df-uni 4801 df-iun 4883 df-br 5031 df-opab 5093 df-mpt 5111 df-tr 5137 df-id 5425 df-eprel 5430 df-po 5438 df-so 5439 df-fr 5478 df-we 5480 df-xp 5525 df-rel 5526 df-cnv 5527 df-co 5528 df-dm 5529 df-rn 5530 df-res 5531 df-ima 5532 df-pred 6116 df-ord 6162 df-on 6163 df-lim 6164 df-suc 6165 df-iota 6283 df-fun 6326 df-fn 6327 df-f 6328 df-f1 6329 df-fo 6330 df-f1o 6331 df-fv 6332 df-ov 7138 df-om 7561 df-wrecs 7930 df-recs 7991 df-rdg 8029 df-nn 11626 df-ndx 16478 df-slot 16479 df-base 16481 |
This theorem is referenced by: ressbas 16546 opelstrbas 16589 1strbas 16591 2strbas 16595 2strbas1 16598 rngbase 16612 srngbase 16620 lmodbase 16629 ipsbase 16636 phlbase 16646 topgrpbas 16654 otpsbas 16661 odrngbas 16672 prdsval 16720 prdsbas 16722 imasbas 16777 oppcbas 16980 rescbas 17091 rescabs 17095 fucbas 17222 setcbas 17330 catcbas 17349 estrcbas 17367 odubas 17735 ipobas 17757 grpss 18113 rmodislmod 19695 islidl 19977 lidlrsppropd 19996 rspsn 20020 cnfldbas 20095 thlbas 20385 psrbas 20616 matbas 21018 tuslem 22873 setsmsbas 23082 trkgbas 26239 setsvtx 26828 idlsrgbas 31057 algbase 40122 cznrnglem 44577 cznabel 44578 rngcbasALTV 44607 ringcbasALTV 44670 |
Copyright terms: Public domain | W3C validator |