Colors of
variables: wff
setvar class |
Syntax hints:
β wi 4 β§ w3a 1088
β wcel 2107 Γ
cxp 5675 βΆwf 6540
βcfv 6544 (class class class)co 7409
β*cxr 11247
βMetcxmet 20929 |
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-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 ax-sep 5300 ax-nul 5307 ax-pow 5364 ax-pr 5428 ax-un 7725 ax-cnex 11166 ax-resscn 11167 |
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-nf 1787 df-sb 2069 df-mo 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ne 2942 df-ral 3063 df-rex 3072 df-rab 3434 df-v 3477 df-sbc 3779 df-dif 3952 df-un 3954 df-in 3956 df-ss 3966 df-nul 4324 df-if 4530 df-pw 4605 df-sn 4630 df-pr 4632 df-op 4636 df-uni 4910 df-br 5150 df-opab 5212 df-mpt 5233 df-id 5575 df-xp 5683 df-rel 5684 df-cnv 5685 df-co 5686 df-dm 5687 df-rn 5688 df-iota 6496 df-fun 6546 df-fn 6547 df-f 6548 df-fv 6552 df-ov 7412 df-oprab 7413 df-mpo 7414 df-map 8822 df-xr 11252 df-xmet 20937 |
This theorem is referenced by: xmetge0
23850 xmetlecl
23852 xmetsym
23853 xmetrtri
23861 xmetrtri2
23862 xmetgt0
23864 prdsdsf
23873 prdsxmetlem
23874 imasdsf1olem
23879 imasf1oxmet
23881 xpsdsval
23887 xblpnf
23902 bldisj
23904 blgt0
23905 xblss2
23908 blhalf
23911 xbln0
23920 blin
23927 blss
23931 xmscl
23968 prdsbl
24000 blsscls2
24013 blcld
24014 blcls
24015 comet
24022 stdbdxmet
24024 stdbdmet
24025 stdbdbl
24026 tmsxpsval2
24048 metcnpi3
24055 txmetcnp
24056 xrsmopn
24328 metdcnlem
24352 metdsf
24364 metdsge
24365 metdstri
24367 metdsle
24368 metdscnlem
24371 metnrmlem1
24375 metnrmlem3
24377 lmnn
24780 iscfil2
24783 iscau3
24795 dvlip2
25512 heicant
36523 |