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| Mirrors > Home > MPE Home > Th. List > basendx | Structured version Visualization version GIF version | ||
| Description: Index value of the base set extractor. (Contributed by Mario Carneiro, 2-Aug-2013.) Use of this theorem is discouraged since the particular value 1 for the index is an implementation detail, see section header comment mmtheorems.html#cnx for more information. (New usage is discouraged.) |
| Ref | Expression |
|---|---|
| basendx | ⊢ (Base‘ndx) = 1 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-base 17248 | . 2 ⊢ Base = Slot 1 | |
| 2 | 1nn 12277 | . 2 ⊢ 1 ∈ ℕ | |
| 3 | 1, 2 | ndxarg 17233 | 1 ⊢ (Base‘ndx) = 1 |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 ‘cfv 6561 1c1 11156 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: basendxnn 17257 1strstr 17261 2strstr 17267 2strstr1OLD 17271 resslemOLD 17288 basendxltplusgndx 17326 grpbasex 17335 grpplusgx 17336 basendxnmulrndx 17339 rngstr 17342 starvndxnbasendx 17348 scandxnbasendx 17360 vscandxnbasendx 17365 lmodstr 17369 ipndxnbasendx 17376 basendxlttsetndx 17399 topgrpstr 17405 basendxltplendx 17413 otpsstr 17420 basendxnocndx 17427 basendxltdsndx 17432 basendxltunifndx 17442 slotsbhcdif 17459 rescabsOLD 17878 catstr 18005 odubasOLD 18337 ipostr 18574 cnfldfunALTOLDOLD 21393 thlbasOLD 21715 indistpsx 23017 tuslemOLD 24276 setsmsbasOLD 24486 slotsinbpsd 28449 slotslnbpsd 28450 trkgstr 28452 eengstr 28995 basendxltedgfndx 29010 |
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