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Mirrors > Home > MPE Home > Th. List > lspsnel5 | Structured version Visualization version Unicode version |
Description: Relationship between a vector and the 1-dim (or 0-dim) subspace it generates. (Contributed by NM, 8-Aug-2014.) |
Ref | Expression |
---|---|
lspsnel5.v | |
lspsnel5.s | |
lspsnel5.n | |
lspsnel5.w | |
lspsnel5.a | |
lspsnel5.x |
Ref | Expression |
---|---|
lspsnel5 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lspsnel5.v | . . 3 | |
2 | lspsnel5.s | . . 3 | |
3 | lspsnel5.n | . . 3 | |
4 | lspsnel5.w | . . 3 | |
5 | lspsnel5.a | . . 3 | |
6 | 1, 2, 3, 4, 5 | lspsnel6 18994 | . 2 |
7 | lspsnel5.x | . . 3 | |
8 | 7 | biantrurd 529 | . 2 |
9 | 6, 8 | bitr4d 271 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wcel 1990 wss 3574 csn 4177 cfv 5888 cbs 15857 clmod 18863 clss 18932 clspn 18971 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-rep 4771 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 df-rmo 2920 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-int 4476 df-iun 4522 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-riota 6611 df-ov 6653 df-0g 16102 df-mgm 17242 df-sgrp 17284 df-mnd 17295 df-grp 17425 df-lmod 18865 df-lss 18933 df-lsp 18972 |
This theorem is referenced by: lspsnel5a 18996 lspprid1 18997 lspsnss2 19005 lsmelpr 19091 lspsncmp 19116 lspsnne1 19117 lspsnne2 19118 lspsneq 19122 lspindpi 19132 islbs2 19154 lindsenlbs 33404 lsatelbN 34293 lsmsat 34295 lsatfixedN 34296 l1cvpat 34341 dia2dimlem5 36357 dochsncom 36671 dihjat1lem 36717 dvh4dimlem 36732 lclkrlem2a 36796 lcfrlem6 36836 lcfrlem20 36851 lcfrlem26 36857 lcfrlem36 36867 mapdval2N 36919 mapdrvallem2 36934 mapdindp 36960 mapdh6aN 37024 lspindp5 37059 mapdh8ab 37066 mapdh8e 37073 hdmap1l6a 37099 hdmaprnlem3eN 37150 hdmapoc 37223 |
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