![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > itvndx | Structured version Visualization version GIF version |
Description: Index value of the Interval (segment) slot. Use ndxarg 17193. (Contributed by Thierry Arnoux, 24-Aug-2017.) (New usage is discouraged.) |
Ref | Expression |
---|---|
itvndx | ⊢ (Itv‘ndx) = ;16 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-itv 28354 | . 2 ⊢ Itv = Slot ;16 | |
2 | 1nn0 12535 | . . 3 ⊢ 1 ∈ ℕ0 | |
3 | 6nn 12348 | . . 3 ⊢ 6 ∈ ℕ | |
4 | 2, 3 | decnncl 12744 | . 2 ⊢ ;16 ∈ ℕ |
5 | 1, 4 | ndxarg 17193 | 1 ⊢ (Itv‘ndx) = ;16 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 ‘cfv 6553 1c1 11155 6c6 12318 ;cdc 12724 ndxcnx 17190 Itvcitv 28352 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2166 ax-ext 2696 ax-sep 5303 ax-nul 5310 ax-pow 5368 ax-pr 5432 ax-un 7745 ax-cnex 11210 ax-resscn 11211 ax-1cn 11212 ax-icn 11213 ax-addcl 11214 ax-addrcl 11215 ax-mulcl 11216 ax-mulrcl 11217 ax-mulcom 11218 ax-addass 11219 ax-mulass 11220 ax-distr 11221 ax-i2m1 11222 ax-1ne0 11223 ax-1rid 11224 ax-rnegex 11225 ax-rrecex 11226 ax-cnre 11227 ax-pre-lttri 11228 ax-pre-lttrn 11229 ax-pre-ltadd 11230 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-3or 1085 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2528 df-eu 2557 df-clab 2703 df-cleq 2717 df-clel 2802 df-nfc 2877 df-ne 2930 df-nel 3036 df-ral 3051 df-rex 3060 df-reu 3364 df-rab 3419 df-v 3463 df-sbc 3776 df-csb 3892 df-dif 3949 df-un 3951 df-in 3953 df-ss 3963 df-pss 3966 df-nul 4325 df-if 4533 df-pw 4608 df-sn 4633 df-pr 4635 df-op 4639 df-uni 4913 df-iun 5002 df-br 5153 df-opab 5215 df-mpt 5236 df-tr 5270 df-id 5579 df-eprel 5585 df-po 5593 df-so 5594 df-fr 5636 df-we 5638 df-xp 5687 df-rel 5688 df-cnv 5689 df-co 5690 df-dm 5691 df-rn 5692 df-res 5693 df-ima 5694 df-pred 6311 df-ord 6378 df-on 6379 df-lim 6380 df-suc 6381 df-iota 6505 df-fun 6555 df-fn 6556 df-f 6557 df-f1 6558 df-fo 6559 df-f1o 6560 df-fv 6561 df-ov 7426 df-om 7876 df-2nd 8003 df-frecs 8295 df-wrecs 8326 df-recs 8400 df-rdg 8439 df-er 8733 df-en 8974 df-dom 8975 df-sdom 8976 df-pnf 11296 df-mnf 11297 df-ltxr 11299 df-nn 12260 df-2 12322 df-3 12323 df-4 12324 df-5 12325 df-6 12326 df-7 12327 df-8 12328 df-9 12329 df-n0 12520 df-dec 12725 df-slot 17179 df-ndx 17191 df-itv 28354 |
This theorem is referenced by: slotsinbpsd 28360 lngndxnitvndx 28362 trkgstr 28363 ttgvalOLD 28795 ttglemOLD 28797 eengstr 28906 |
Copyright terms: Public domain | W3C validator |