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| Mirrors > Home > MPE Home > Th. List > baseid | Structured version Visualization version GIF version | ||
| Description: Utility theorem: index-independent form of df-base 17248. (Contributed by NM, 20-Oct-2012.) |
| Ref | Expression |
|---|---|
| baseid | ⊢ Base = Slot (Base‘ndx) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-base 17248 | . 2 ⊢ Base = Slot 1 | |
| 2 | 1nn 12277 | . 2 ⊢ 1 ∈ ℕ | |
| 3 | 1, 2 | ndxid 17234 | 1 ⊢ Base = Slot (Base‘ndx) |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 ‘cfv 6561 1c1 11156 Slot cslot 17218 ndxcnx 17230 Basecbs 17247 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-10 2141 ax-11 2157 ax-12 2177 ax-ext 2708 ax-sep 5296 ax-nul 5306 ax-pow 5365 ax-pr 5432 ax-un 7755 ax-cnex 11211 ax-1cn 11213 ax-addcl 11215 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3or 1088 df-3an 1089 df-tru 1543 df-fal 1553 df-ex 1780 df-nf 1784 df-sb 2065 df-mo 2540 df-eu 2569 df-clab 2715 df-cleq 2729 df-clel 2816 df-nfc 2892 df-ne 2941 df-ral 3062 df-rex 3071 df-reu 3381 df-rab 3437 df-v 3482 df-sbc 3789 df-csb 3900 df-dif 3954 df-un 3956 df-in 3958 df-ss 3968 df-pss 3971 df-nul 4334 df-if 4526 df-pw 4602 df-sn 4627 df-pr 4629 df-op 4633 df-uni 4908 df-iun 4993 df-br 5144 df-opab 5206 df-mpt 5226 df-tr 5260 df-id 5578 df-eprel 5584 df-po 5592 df-so 5593 df-fr 5637 df-we 5639 df-xp 5691 df-rel 5692 df-cnv 5693 df-co 5694 df-dm 5695 df-rn 5696 df-res 5697 df-ima 5698 df-pred 6321 df-ord 6387 df-on 6388 df-lim 6389 df-suc 6390 df-iota 6514 df-fun 6563 df-fn 6564 df-f 6565 df-f1 6566 df-fo 6567 df-f1o 6568 df-fv 6569 df-ov 7434 df-om 7888 df-2nd 8015 df-frecs 8306 df-wrecs 8337 df-recs 8411 df-rdg 8450 df-nn 12267 df-slot 17219 df-ndx 17231 df-base 17248 |
| This theorem is referenced by: basfn 17251 base0 17252 basndxelwund 17258 opelstrbas 17260 1strbas 17263 1strbasOLD 17264 2strbas 17268 2strbas1 17272 ressbas 17280 ressbasOLD 17281 ressval3d 17292 wunress 17295 wunressOLD 17296 rngbase 17343 srngbase 17354 lmodbase 17370 ipsbase 17381 phlbase 17391 topgrpbas 17406 otpsbas 17421 odrngbas 17448 prdsval 17500 prdsbas 17502 imasbas 17557 oppcbas 17761 rescbas 17873 rescabs 17877 rescabsOLD 17878 wunfunc 17946 wunnat 18004 fucbas 18008 setcbas 18123 catcbas 18146 catcbaselcl 18159 catcfuccl 18163 estrcbas 18169 estrcbasbas 18175 estrreslem1 18181 catcxpccl 18252 odubas 18336 odubasOLD 18337 ipobas 18576 grpss 18972 oppgbas 19370 mgpbas 20142 opprbas 20341 ringcbasbas 20673 rmodislmod 20928 srabase 21177 rlmscaf 21214 islidl 21225 lidlrsppropd 21254 rspsn 21343 cnfldbas 21368 cnfldbasOLD 21383 zlmbas 21529 znbas2 21555 thlbas 21714 thlbasOLD 21715 psrbas 21953 opsrbas 22069 ply1tmcl 22275 ply1scltm 22284 ply1sclf 22288 ply1scl0OLD 22294 ply1scl1OLD 22297 matbas 22417 tuslem 24275 tuslemOLD 24276 setsmsbas 24485 setsmsbasOLD 24486 tngbas 24655 nrgtrg 24711 trkgbas 28453 ttgbas 28887 setsvtx 29052 rlocbas 33271 rlocaddval 33272 rlocmulval 33273 resvbas 33359 idlsrgbas 33532 bj-endbase 37317 hlhilsbase 41942 opprmndb 42521 opprgrpb 42522 opprablb 42523 algbase 43186 mnringbased 44230 cznrnglem 48175 cznabel 48176 rngcbasALTV 48182 ringcbasALTV 48216 ringcbasbasALTV 48228 prstcbas 49156 mndtcbasval 49177 |
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