Colors of
variables: wff
setvar class |
Syntax hints:
β wi 4 β wcel 2106
β wne 2940 βwral 3061 β
c0 4322
βcfv 6543 (class class class)co 7411
Metcmet 21130 MetOpencmopn 21134 fLim cflim 23658 CauFilccfil 24993 CMetccmet 24995 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913
ax-6 1971 ax-7 2011 ax-8 2108
ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2703 ax-sep 5299 ax-nul 5306 ax-pr 5427 |
This theorem depends on definitions:
df-bi 206 df-an 397
df-or 846 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-mo 2534 df-eu 2563 df-clab 2710 df-cleq 2724 df-clel 2810 df-nfc 2885 df-ne 2941 df-ral 3062 df-rex 3071 df-rab 3433 df-v 3476 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-nul 4323 df-if 4529 df-sn 4629 df-pr 4631 df-op 4635 df-uni 4909 df-br 5149 df-opab 5211 df-mpt 5232 df-id 5574 df-xp 5682 df-rel 5683 df-cnv 5684 df-co 5685 df-dm 5686 df-iota 6495 df-fun 6545 df-fv 6551 df-ov 7414 df-cmet 24998 |
This theorem is referenced by: cmetmeti
25028 cmetcaulem
25029 cmetcau
25030 iscmet2
25035 metsscmetcld
25056 cmetss
25057 bcthlem2
25066 bcthlem3
25067 bcthlem4
25068 bcthlem5
25069 bcth2
25071 bcth3
25072 cmetcusp1
25094 cmetcusp
25095 minveclem3
25170 ubthlem1
30378 ubthlem2
30379 hlmet
30403 fmcncfil
33197 heiborlem3
36984 heiborlem6
36987 heiborlem8
36989 heiborlem9
36990 heiborlem10
36991 heibor
36992 bfplem1
36993 bfplem2
36994 bfp
36995 |