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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 17246 | . 2 ⊢ Base = Slot 1 | |
2 | 1nn 12275 | . 2 ⊢ 1 ∈ ℕ | |
3 | 1, 2 | ndxarg 17230 | 1 ⊢ (Base‘ndx) = 1 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 ‘cfv 6563 1c1 11154 ndxcnx 17227 Basecbs 17245 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-10 2139 ax-11 2155 ax-12 2175 ax-ext 2706 ax-sep 5302 ax-nul 5312 ax-pow 5371 ax-pr 5438 ax-un 7754 ax-cnex 11209 ax-1cn 11211 ax-addcl 11213 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3or 1087 df-3an 1088 df-tru 1540 df-fal 1550 df-ex 1777 df-nf 1781 df-sb 2063 df-mo 2538 df-eu 2567 df-clab 2713 df-cleq 2727 df-clel 2814 df-nfc 2890 df-ne 2939 df-ral 3060 df-rex 3069 df-reu 3379 df-rab 3434 df-v 3480 df-sbc 3792 df-csb 3909 df-dif 3966 df-un 3968 df-in 3970 df-ss 3980 df-pss 3983 df-nul 4340 df-if 4532 df-pw 4607 df-sn 4632 df-pr 4634 df-op 4638 df-uni 4913 df-iun 4998 df-br 5149 df-opab 5211 df-mpt 5232 df-tr 5266 df-id 5583 df-eprel 5589 df-po 5597 df-so 5598 df-fr 5641 df-we 5643 df-xp 5695 df-rel 5696 df-cnv 5697 df-co 5698 df-dm 5699 df-rn 5700 df-res 5701 df-ima 5702 df-pred 6323 df-ord 6389 df-on 6390 df-lim 6391 df-suc 6392 df-iota 6516 df-fun 6565 df-fn 6566 df-f 6567 df-f1 6568 df-fo 6569 df-f1o 6570 df-fv 6571 df-ov 7434 df-om 7888 df-2nd 8014 df-frecs 8305 df-wrecs 8336 df-recs 8410 df-rdg 8449 df-nn 12265 df-slot 17216 df-ndx 17228 df-base 17246 |
This theorem is referenced by: basendxnn 17255 1strstr 17260 2strstr 17267 2strstr1OLD 17271 resslemOLD 17288 basendxltplusgndx 17327 grpbasex 17337 grpplusgx 17338 basendxnmulrndx 17341 rngstr 17344 starvndxnbasendx 17350 scandxnbasendx 17362 vscandxnbasendx 17367 lmodstr 17371 ipndxnbasendx 17378 basendxlttsetndx 17401 topgrpstr 17407 basendxltplendx 17415 otpsstr 17422 basendxnocndx 17429 basendxltdsndx 17434 basendxltunifndx 17444 slotsbhcdif 17461 oppcbasOLD 17765 rescbasOLD 17878 rescabsOLD 17884 catstr 18013 odubasOLD 18349 ipostr 18587 mgpressOLD 20168 cnfldfunALTOLDOLD 21411 thlbasOLD 21733 indistpsx 23033 tuslemOLD 24292 setsmsbasOLD 24502 slotsinbpsd 28464 slotslnbpsd 28465 trkgstr 28467 eengstr 29010 basendxltedgfndx 29025 |
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