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Mirrors > Home > MPE Home > Th. List > dsid | Structured version Visualization version GIF version |
Description: Utility theorem: index-independent form of df-ds 16328. (Contributed by Mario Carneiro, 23-Dec-2013.) |
Ref | Expression |
---|---|
dsid | ⊢ dist = Slot (dist‘ndx) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ds 16328 | . 2 ⊢ dist = Slot ;12 | |
2 | 1nn0 11637 | . . 3 ⊢ 1 ∈ ℕ0 | |
3 | 2nn 11425 | . . 3 ⊢ 2 ∈ ℕ | |
4 | 2, 3 | decnncl 11843 | . 2 ⊢ ;12 ∈ ℕ |
5 | 1, 4 | ndxid 16249 | 1 ⊢ dist = Slot (dist‘ndx) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1658 ‘cfv 6124 1c1 10254 2c2 11407 ;cdc 11822 ndxcnx 16220 Slot cslot 16222 distcds 16315 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1896 ax-4 1910 ax-5 2011 ax-6 2077 ax-7 2114 ax-8 2168 ax-9 2175 ax-10 2194 ax-11 2209 ax-12 2222 ax-13 2391 ax-ext 2804 ax-sep 5006 ax-nul 5014 ax-pow 5066 ax-pr 5128 ax-un 7210 ax-cnex 10309 ax-resscn 10310 ax-1cn 10311 ax-icn 10312 ax-addcl 10313 ax-addrcl 10314 ax-mulcl 10315 ax-mulrcl 10316 ax-mulcom 10317 ax-addass 10318 ax-mulass 10319 ax-distr 10320 ax-i2m1 10321 ax-1ne0 10322 ax-1rid 10323 ax-rnegex 10324 ax-rrecex 10325 ax-cnre 10326 ax-pre-lttri 10327 ax-pre-lttrn 10328 ax-pre-ltadd 10329 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 881 df-3or 1114 df-3an 1115 df-tru 1662 df-ex 1881 df-nf 1885 df-sb 2070 df-mo 2606 df-eu 2641 df-clab 2813 df-cleq 2819 df-clel 2822 df-nfc 2959 df-ne 3001 df-nel 3104 df-ral 3123 df-rex 3124 df-reu 3125 df-rab 3127 df-v 3417 df-sbc 3664 df-csb 3759 df-dif 3802 df-un 3804 df-in 3806 df-ss 3813 df-pss 3815 df-nul 4146 df-if 4308 df-pw 4381 df-sn 4399 df-pr 4401 df-tp 4403 df-op 4405 df-uni 4660 df-iun 4743 df-br 4875 df-opab 4937 df-mpt 4954 df-tr 4977 df-id 5251 df-eprel 5256 df-po 5264 df-so 5265 df-fr 5302 df-we 5304 df-xp 5349 df-rel 5350 df-cnv 5351 df-co 5352 df-dm 5353 df-rn 5354 df-res 5355 df-ima 5356 df-pred 5921 df-ord 5967 df-on 5968 df-lim 5969 df-suc 5970 df-iota 6087 df-fun 6126 df-fn 6127 df-f 6128 df-f1 6129 df-fo 6130 df-f1o 6131 df-fv 6132 df-ov 6909 df-om 7328 df-wrecs 7673 df-recs 7735 df-rdg 7773 df-er 8010 df-en 8224 df-dom 8225 df-sdom 8226 df-pnf 10394 df-mnf 10395 df-ltxr 10397 df-nn 11352 df-2 11415 df-3 11416 df-4 11417 df-5 11418 df-6 11419 df-7 11420 df-8 11421 df-9 11422 df-n0 11620 df-dec 11823 df-ndx 16226 df-slot 16227 df-ds 16328 |
This theorem is referenced by: odrngds 16426 prdsds 16478 imasds 16527 cnfldds 20117 setsmsds 22652 tngds 22823 trkgdist 25759 ecgrtg 26283 zlmds 30554 |
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