Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > minmar1val0 | Structured version Visualization version Unicode version |
Description: Second substitution for the definition of a matrix for a minor. (Contributed by AV, 31-Dec-2018.) |
Ref | Expression |
---|---|
minmar1fval.a | Mat |
minmar1fval.b | |
minmar1fval.q | minMatR1 |
minmar1fval.o | |
minmar1fval.z |
Ref | Expression |
---|---|
minmar1val0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | minmar1fval.a | . . . . 5 Mat | |
2 | minmar1fval.b | . . . . 5 | |
3 | 1, 2 | matrcl 20218 | . . . 4 |
4 | 3 | simpld 475 | . . 3 |
5 | mpt2exga 7246 | . . 3 | |
6 | 4, 4, 5 | syl2anc 693 | . 2 |
7 | oveq 6656 | . . . . . 6 | |
8 | 7 | ifeq2d 4105 | . . . . 5 |
9 | 8 | mpt2eq3dv 6721 | . . . 4 |
10 | 9 | mpt2eq3dv 6721 | . . 3 |
11 | minmar1fval.q | . . . 4 minMatR1 | |
12 | minmar1fval.o | . . . 4 | |
13 | minmar1fval.z | . . . 4 | |
14 | 1, 2, 11, 12, 13 | minmar1fval 20452 | . . 3 |
15 | 10, 14 | fvmptg 6280 | . 2 |
16 | 6, 15 | mpdan 702 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wcel 1990 cvv 3200 cif 4086 cfv 5888 (class class class)co 6650 cmpt2 6652 cfn 7955 cbs 15857 c0g 16100 cur 18501 Mat cmat 20213 minMatR1 cminmar1 20439 |
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 ax-un 6949 |
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-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-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-ov 6653 df-oprab 6654 df-mpt2 6655 df-1st 7168 df-2nd 7169 df-slot 15861 df-base 15863 df-mat 20214 df-minmar1 20441 |
This theorem is referenced by: minmar1val 20454 minmar1marrep 20456 |
Copyright terms: Public domain | W3C validator |