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Mirrors > Home > MPE Home > Th. List > scandx | Structured version Visualization version GIF version |
Description: Index value of the df-sca 16976 slot. (Contributed by Mario Carneiro, 14-Aug-2015.) (New usage is discouraged.) |
Ref | Expression |
---|---|
scandx | ⊢ (Scalar‘ndx) = 5 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-sca 16976 | . 2 ⊢ Scalar = Slot 5 | |
2 | 5nn 12059 | . 2 ⊢ 5 ∈ ℕ | |
3 | 1, 2 | ndxarg 16895 | 1 ⊢ (Scalar‘ndx) = 5 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 ‘cfv 6432 5c5 12031 ndxcnx 16892 Scalarcsca 16963 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2015 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2158 ax-12 2175 ax-ext 2711 ax-sep 5227 ax-nul 5234 ax-pow 5292 ax-pr 5356 ax-un 7582 ax-cnex 10928 ax-1cn 10930 ax-addcl 10932 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 845 df-3or 1087 df-3an 1088 df-tru 1545 df-fal 1555 df-ex 1787 df-nf 1791 df-sb 2072 df-mo 2542 df-eu 2571 df-clab 2718 df-cleq 2732 df-clel 2818 df-nfc 2891 df-ne 2946 df-ral 3071 df-rex 3072 df-reu 3073 df-rab 3075 df-v 3433 df-sbc 3721 df-csb 3838 df-dif 3895 df-un 3897 df-in 3899 df-ss 3909 df-pss 3911 df-nul 4263 df-if 4466 df-pw 4541 df-sn 4568 df-pr 4570 df-op 4574 df-uni 4846 df-iun 4932 df-br 5080 df-opab 5142 df-mpt 5163 df-tr 5197 df-id 5490 df-eprel 5496 df-po 5504 df-so 5505 df-fr 5545 df-we 5547 df-xp 5596 df-rel 5597 df-cnv 5598 df-co 5599 df-dm 5600 df-rn 5601 df-res 5602 df-ima 5603 df-pred 6201 df-ord 6268 df-on 6269 df-lim 6270 df-suc 6271 df-iota 6390 df-fun 6434 df-fn 6435 df-f 6436 df-f1 6437 df-fo 6438 df-f1o 6439 df-fv 6440 df-ov 7274 df-om 7707 df-2nd 7825 df-frecs 8088 df-wrecs 8119 df-recs 8193 df-rdg 8232 df-nn 11974 df-2 12036 df-3 12037 df-4 12038 df-5 12039 df-slot 16881 df-ndx 16893 df-sca 16976 |
This theorem is referenced by: scandxnbasendx 17024 scandxnplusgndx 17025 scandxnmulrndx 17026 vscandxnscandx 17032 lmodstr 17033 slotsdifipndx 17043 ipsstr 17044 slotstnscsi 17068 plendxnscandx 17081 slotsdnscsi 17100 rmodislmodOLD 20190 sralemOLD 20438 srascaOLD 20446 zlmlemOLD 20717 psrvalstr 21117 matscaOLD 21561 resvlemOLD 31527 zlmdsOLD 31909 zlmtsetOLD 31911 algstr 40999 |
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