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Mirrors > Home > MPE Home > Th. List > vscandx | Structured version Visualization version GIF version |
Description: Index value of the df-vsca 16438 slot. (Contributed by Mario Carneiro, 14-Aug-2015.) |
Ref | Expression |
---|---|
vscandx | ⊢ ( ·𝑠 ‘ndx) = 6 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-vsca 16438 | . 2 ⊢ ·𝑠 = Slot 6 | |
2 | 6nn 11532 | . 2 ⊢ 6 ∈ ℕ | |
3 | 1, 2 | ndxarg 16364 | 1 ⊢ ( ·𝑠 ‘ndx) = 6 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1507 ‘cfv 6188 6c6 11499 ndxcnx 16336 ·𝑠 cvsca 16425 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1758 ax-4 1772 ax-5 1869 ax-6 1928 ax-7 1965 ax-8 2052 ax-9 2059 ax-10 2079 ax-11 2093 ax-12 2106 ax-13 2301 ax-ext 2751 ax-sep 5060 ax-nul 5067 ax-pow 5119 ax-pr 5186 ax-un 7279 ax-cnex 10391 ax-1cn 10393 ax-addcl 10395 |
This theorem depends on definitions: df-bi 199 df-an 388 df-or 834 df-3or 1069 df-3an 1070 df-tru 1510 df-ex 1743 df-nf 1747 df-sb 2016 df-mo 2547 df-eu 2584 df-clab 2760 df-cleq 2772 df-clel 2847 df-nfc 2919 df-ne 2969 df-ral 3094 df-rex 3095 df-reu 3096 df-rab 3098 df-v 3418 df-sbc 3683 df-csb 3788 df-dif 3833 df-un 3835 df-in 3837 df-ss 3844 df-pss 3846 df-nul 4180 df-if 4351 df-pw 4424 df-sn 4442 df-pr 4444 df-tp 4446 df-op 4448 df-uni 4713 df-iun 4794 df-br 4930 df-opab 4992 df-mpt 5009 df-tr 5031 df-id 5312 df-eprel 5317 df-po 5326 df-so 5327 df-fr 5366 df-we 5368 df-xp 5413 df-rel 5414 df-cnv 5415 df-co 5416 df-dm 5417 df-rn 5418 df-res 5419 df-ima 5420 df-pred 5986 df-ord 6032 df-on 6033 df-lim 6034 df-suc 6035 df-iota 6152 df-fun 6190 df-fn 6191 df-f 6192 df-f1 6193 df-fo 6194 df-f1o 6195 df-fv 6196 df-ov 6979 df-om 7397 df-wrecs 7750 df-recs 7812 df-rdg 7850 df-nn 11440 df-2 11503 df-3 11504 df-4 11505 df-5 11506 df-6 11507 df-ndx 16342 df-slot 16343 df-vsca 16438 |
This theorem is referenced by: lmodstr 16492 ipsstr 16499 rmodislmod 19424 sralem 19671 srasca 19675 sravsca 19676 psrvalstr 19857 zlmlem 20366 zlmsca 20370 matvsca 20729 zlmds 30846 zlmtset 30847 algstr 39170 |
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