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Mirrors > Home > MPE Home > Th. List > matbas0 | Structured version Visualization version Unicode version |
Description: There is no matrix for a not finite dimension or a proper class as the underlying ring. (Contributed by AV, 28-Dec-2018.) |
Ref | Expression |
---|---|
matbas0 | Mat |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mat 20214 | . . . 4 Mat freeLMod sSet maMul | |
2 | 1 | mpt2ndm0 6875 | . . 3 Mat |
3 | 2 | fveq2d 6195 | . 2 Mat |
4 | base0 15912 | . 2 | |
5 | 3, 4 | syl6eqr 2674 | 1 Mat |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wa 384 wceq 1483 wcel 1990 cvv 3200 c0 3915 cop 4183 cotp 4185 cxp 5112 cfv 5888 (class class class)co 6650 cfn 7955 cnx 15854 sSet csts 15855 cbs 15857 cmulr 15942 freeLMod cfrlm 20090 maMul cmmul 20189 Mat cmat 20213 |
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-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-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 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-iota 5851 df-fun 5890 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-slot 15861 df-base 15863 df-mat 20214 |
This theorem is referenced by: nfimdetndef 20395 mdetfval1 20396 |
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