Colors of
variables: wff
setvar class |
Syntax hints:
β wi 4 β wb 205
β§ wa 397 = wceq 1542
β wcel 2107 βwral 3062 class class class wbr 5149
Γ cxp 5675 βΆwf 6540 βcfv 6544
(class class class)co 7409 βcr 11109
0cc0 11110 + caddc 11113 β€ cle 11249
Metcmet 20930 |
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-met 20938 |
This theorem is referenced by: metcl
23838 metn0
23866 metres2
23869 metres
23871 msf
23964 isngp3
24107 tngngp2
24169 tngngpim
24176 xrsdsre
24326 metdcn2
24355 cncms
24872 cnrrext
32990 isbnd3
36652 isbnd3b
36653 ssbnd
36656 bnd2lem
36659 prdsbnd
36661 |