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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 17172 | . 2 ⊢ Base = Slot 1 | |
2 | 1nn 12245 | . 2 ⊢ 1 ∈ ℕ | |
3 | 1, 2 | ndxarg 17156 | 1 ⊢ (Base‘ndx) = 1 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1534 ‘cfv 6542 1c1 11131 ndxcnx 17153 Basecbs 17171 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-10 2130 ax-11 2147 ax-12 2164 ax-ext 2698 ax-sep 5293 ax-nul 5300 ax-pow 5359 ax-pr 5423 ax-un 7734 ax-cnex 11186 ax-1cn 11188 ax-addcl 11190 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 847 df-3or 1086 df-3an 1087 df-tru 1537 df-fal 1547 df-ex 1775 df-nf 1779 df-sb 2061 df-mo 2529 df-eu 2558 df-clab 2705 df-cleq 2719 df-clel 2805 df-nfc 2880 df-ne 2936 df-ral 3057 df-rex 3066 df-reu 3372 df-rab 3428 df-v 3471 df-sbc 3775 df-csb 3890 df-dif 3947 df-un 3949 df-in 3951 df-ss 3961 df-pss 3963 df-nul 4319 df-if 4525 df-pw 4600 df-sn 4625 df-pr 4627 df-op 4631 df-uni 4904 df-iun 4993 df-br 5143 df-opab 5205 df-mpt 5226 df-tr 5260 df-id 5570 df-eprel 5576 df-po 5584 df-so 5585 df-fr 5627 df-we 5629 df-xp 5678 df-rel 5679 df-cnv 5680 df-co 5681 df-dm 5682 df-rn 5683 df-res 5684 df-ima 5685 df-pred 6299 df-ord 6366 df-on 6367 df-lim 6368 df-suc 6369 df-iota 6494 df-fun 6544 df-fn 6545 df-f 6546 df-f1 6547 df-fo 6548 df-f1o 6549 df-fv 6550 df-ov 7417 df-om 7865 df-2nd 7988 df-frecs 8280 df-wrecs 8311 df-recs 8385 df-rdg 8424 df-nn 12235 df-slot 17142 df-ndx 17154 df-base 17172 |
This theorem is referenced by: basendxnn 17181 1strstr 17186 2strstr 17193 2strstr1OLD 17197 resslemOLD 17214 basendxltplusgndx 17253 grpbasex 17263 grpplusgx 17264 basendxnmulrndx 17267 rngstr 17270 starvndxnbasendx 17276 scandxnbasendx 17288 vscandxnbasendx 17293 lmodstr 17297 ipndxnbasendx 17304 basendxlttsetndx 17327 topgrpstr 17333 basendxltplendx 17341 otpsstr 17348 basendxnocndx 17355 basendxltdsndx 17360 basendxltunifndx 17370 slotsbhcdif 17387 oppcbasOLD 17691 rescbasOLD 17804 rescabsOLD 17810 catstr 17939 odubasOLD 18275 ipostr 18512 mgpressOLD 20081 cnfldfunALTOLDOLD 21295 thlbasOLD 21616 indistpsx 22900 tuslemOLD 24159 setsmsbasOLD 24369 slotsinbpsd 28232 slotslnbpsd 28233 trkgstr 28235 eengstr 28778 basendxltedgfndx 28793 |
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