Colors of
variables: wff
setvar class |
Syntax hints:
β wi 4 β wcel 2107
β wne 2940 βwral 3061 β
c0 4286
βcfv 6500 (class class class)co 7361
Metcmet 20805 MetOpencmopn 20809 fLim cflim 23308 CauFilccfil 24639 CMetccmet 24641 |
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 5260 ax-nul 5267 ax-pr 5388 |
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 2941 df-ral 3062 df-rex 3071 df-rab 3407 df-v 3449 df-dif 3917 df-un 3919 df-in 3921 df-ss 3931 df-nul 4287 df-if 4491 df-sn 4591 df-pr 4593 df-op 4597 df-uni 4870 df-br 5110 df-opab 5172 df-mpt 5193 df-id 5535 df-xp 5643 df-rel 5644 df-cnv 5645 df-co 5646 df-dm 5647 df-iota 6452 df-fun 6502 df-fv 6508 df-ov 7364 df-cmet 24644 |
This theorem is referenced by: cmetmeti
24674 cmetcaulem
24675 cmetcau
24676 iscmet2
24681 metsscmetcld
24702 cmetss
24703 bcthlem2
24712 bcthlem3
24713 bcthlem4
24714 bcthlem5
24715 bcth2
24717 bcth3
24718 cmetcusp1
24740 cmetcusp
24741 minveclem3
24816 ubthlem1
29861 ubthlem2
29862 hlmet
29886 fmcncfil
32576 heiborlem3
36322 heiborlem6
36325 heiborlem8
36327 heiborlem9
36328 heiborlem10
36329 heibor
36330 bfplem1
36331 bfplem2
36332 bfp
36333 |