Colors of
variables: wff
setvar class |
Syntax hints:
β wi 4 β wcel 2107
β wss 3949 β
ccom 5681 βcfv 6544
distcds 17206 Grpcgrp 18819
-gcsg 18821
MetSpcms 23824 normcnm 24085
NrmGrpcngp 24086 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914
ax-6 1972 ax-7 2012 ax-8 2109
ax-9 2117 ax-ext 2704 |
This theorem depends on definitions:
df-bi 206 df-an 398
df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-rab 3434 df-v 3477 df-dif 3952 df-un 3954 df-in 3956 df-ss 3966 df-nul 4324 df-if 4530 df-sn 4630 df-pr 4632 df-op 4636 df-uni 4910 df-br 5150 df-opab 5212 df-co 5686 df-iota 6496 df-fv 6552 df-ngp 24092 |
This theorem is referenced by: ngpds
24113 ngpds2
24115 ngpds3
24117 ngprcan
24119 isngp4
24121 ngpinvds
24122 ngpsubcan
24123 nmf
24124 nmge0
24126 nmeq0
24127 nminv
24130 nmmtri
24131 nmsub
24132 nmrtri
24133 nm2dif
24134 nmtri
24135 nmtri2
24136 ngpi
24137 nm0
24138 ngptgp
24145 tngngp2
24169 tnggrpr
24172 nrmtngnrm
24175 nlmdsdi
24198 nlmdsdir
24199 nrginvrcnlem
24208 ngpocelbl
24221 nmo0
24252 nmotri
24256 0nghm
24258 nmoid
24259 idnghm
24260 nmods
24261 nmcn
24360 nmoleub2lem2
24632 nmhmcn
24636 cphpyth
24733 cphipval2
24758 4cphipval2
24759 cphipval
24760 ipcnlem2
24761 nglmle
24819 qqhcn
32971 |