Colors of
variables: wff
setvar class |
Syntax hints:
= wceq 1542 ∈ wcel 2107
(class class class)co 7358 ℂcc 11050
0cc0 11052 − cmin 11386
-cneg 11387 |
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 2708 ax-sep 5257 ax-nul 5264 ax-pow 5321 ax-pr 5385 ax-un 7673 ax-resscn 11109 ax-1cn 11110 ax-icn 11111 ax-addcl 11112 ax-addrcl 11113 ax-mulcl 11114 ax-mulrcl 11115 ax-mulcom 11116 ax-addass 11117 ax-mulass 11118 ax-distr 11119 ax-i2m1 11120 ax-1ne0 11121 ax-1rid 11122 ax-rnegex 11123 ax-rrecex 11124 ax-cnre 11125 ax-pre-lttri 11126 ax-pre-lttrn 11127 ax-pre-ltadd 11128 |
This theorem depends on definitions:
df-bi 206 df-an 398
df-or 847 df-3or 1089 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2539 df-eu 2568 df-clab 2715 df-cleq 2729 df-clel 2815 df-nfc 2890 df-ne 2945 df-nel 3051 df-ral 3066 df-rex 3075 df-reu 3355 df-rab 3409 df-v 3448 df-sbc 3741 df-csb 3857 df-dif 3914 df-un 3916 df-in 3918 df-ss 3928 df-nul 4284 df-if 4488 df-pw 4563 df-sn 4588 df-pr 4590 df-op 4594 df-uni 4867 df-br 5107 df-opab 5169 df-mpt 5190 df-id 5532 df-po 5546 df-so 5547 df-xp 5640 df-rel 5641 df-cnv 5642 df-co 5643 df-dm 5644 df-rn 5645 df-res 5646 df-ima 5647 df-iota 6449 df-fun 6499 df-fn 6500 df-f 6501 df-f1 6502 df-fo 6503 df-f1o 6504 df-fv 6505 df-riota 7314 df-ov 7361 df-oprab 7362 df-mpo 7363 df-er 8649 df-en 8885 df-dom 8886 df-sdom 8887 df-pnf 11192 df-mnf 11193 df-ltxr 11195 df-sub 11388 df-neg 11389 |
This theorem is referenced by: negeq0
11456 lt0neg1
11662 lt0neg2
11663 le0neg1
11664 le0neg2
11665 neg1lt0
12271 elznn0
12515 znegcl
12539 xneg0
13132 expneg
13976 sqeqd
15052 sqrmo
15137 0risefac
15922 sin0
16032 m1bits
16321 lcmneg
16480 pcneg
16747 mulgneg
18895 mulgneg2
18911 iblrelem
25158 itgrevallem1
25162 ditg0
25220 ditgneg
25224 logtayl
26018 dcubic2
26197 atan0
26261 atancj
26263 ppiub
26555 lgsneg1
26673 rpvmasum2
26863 ostth3
26989 divnumden2
31717 archirngz
32028 ccfldextdgrr
32359 xrge0iif1
32522 fsum2dsub
33223 bj-pinftyccb
35695 bj-minftyccb
35699 itgaddnclem2
36140 ftc1anclem5
36158 areacirc
36174 monotoddzzfi
41269 acongeq
41310 sqwvfourb
44477 etransclem46
44528 sigariz
45111 sigarcol
45112 sigaradd
45114 |