Colors of
variables: wff
setvar class |
Syntax hints:
β wi 4 β wb 205
β§ wa 394 = wceq 1539
β wcel 2104 βwral 3059 {crab 3430
class class class wbr 5147 βcfv 6542
(class class class)co 7411 βm
cmap 8822 0cc0 11112
+ caddc 11115 Β·
cmul 11117 +βcpnf 11249
β€ cle 11253 [,)cico 13330
Basecbs 17148 +gcplusg 17201 .rcmulr 17202 0gc0g 17389 Ringcrg 20127
AbsValcabv 20567 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1911
ax-6 1969 ax-7 2009 ax-8 2106
ax-9 2114 ax-10 2135 ax-11 2152 ax-12 2169 ax-ext 2701 ax-sep 5298 ax-nul 5305 ax-pr 5426 |
This theorem depends on definitions:
df-bi 206 df-an 395
df-or 844 df-3an 1087 df-tru 1542 df-fal 1552 df-ex 1780 df-nf 1784 df-sb 2066 df-mo 2532 df-eu 2561 df-clab 2708 df-cleq 2722 df-clel 2808 df-nfc 2883 df-ral 3060 df-rex 3069 df-rab 3431 df-v 3474 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-nul 4322 df-if 4528 df-sn 4628 df-pr 4630 df-op 4634 df-uni 4908 df-br 5148 df-opab 5210 df-mpt 5231 df-xp 5681 df-rel 5682 df-cnv 5683 df-dm 5685 df-rn 5686 df-res 5687 df-ima 5688 df-iota 6494 df-fv 6550 df-abv 20568 |
This theorem is referenced by: abvfge0
20573 abveq0
20577 abvmul
20580 abvtri
20581 abv0
20582 abv1z
20583 abvneg
20585 abvsubtri
20586 abvpropd
20593 abvmet
24304 nrgring
24400 tngnrg
24411 abvcxp
27354 |