Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ↔ wb 205
= wceq 1539 ∈
wcel 2104 (class class class)co 7411
ℂcc 11110 0cc0 11112
− cmin 11448 |
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-pow 5362 ax-pr 5426 ax-un 7727 ax-resscn 11169 ax-1cn 11170 ax-icn 11171 ax-addcl 11172 ax-addrcl 11173 ax-mulcl 11174 ax-mulrcl 11175 ax-mulcom 11176 ax-addass 11177 ax-mulass 11178 ax-distr 11179 ax-i2m1 11180 ax-1ne0 11181 ax-1rid 11182 ax-rnegex 11183 ax-rrecex 11184 ax-cnre 11185 ax-pre-lttri 11186 ax-pre-lttrn 11187 ax-pre-ltadd 11188 |
This theorem depends on definitions:
df-bi 206 df-an 395
df-or 844 df-3or 1086 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-ne 2939 df-nel 3045 df-ral 3060 df-rex 3069 df-reu 3375 df-rab 3431 df-v 3474 df-sbc 3777 df-csb 3893 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-nul 4322 df-if 4528 df-pw 4603 df-sn 4628 df-pr 4630 df-op 4634 df-uni 4908 df-br 5148 df-opab 5210 df-mpt 5231 df-id 5573 df-po 5587 df-so 5588 df-xp 5681 df-rel 5682 df-cnv 5683 df-co 5684 df-dm 5685 df-rn 5686 df-res 5687 df-ima 5688 df-iota 6494 df-fun 6544 df-fn 6545 df-f 6546 df-f1 6547 df-fo 6548 df-f1o 6549 df-fv 6550 df-riota 7367 df-ov 7414 df-oprab 7415 df-mpo 7416 df-er 8705 df-en 8942 df-dom 8943 df-sdom 8944 df-pnf 11254 df-mnf 11255 df-ltxr 11257 df-sub 11450 |
This theorem is referenced by: subne0ad
11586 subeq0bd
11644 muleqadd
11862 mulcan1g
11871 ofsubeq0
12213 nn0n0n1ge2
12543 mod0
13845 modirr
13911 addmodlteq
13915 sqreulem
15310 sqreu
15311 tanaddlem
16113 fldivp1
16834 4sqlem11
16892 4sqlem16
16897 znf1o
21326 cphsqrtcl2
24934 rrxmet
25156 dvcobr
25697 dvcobrOLD
25698 dvcnvlem
25728 cmvth
25743 dvlip
25745 lhop1lem
25765 ftc1lem5
25792 aalioulem2
26082 sineq0
26269 tanarg
26363 affineequiv
26564 quad2
26580 dcubic
26587 eqeelen
28429 colinearalg
28435 axcontlem7
28495 ipasslem9
30358 ip2eqi
30376 hi2eq
30625 lnopeqi
31528 riesz3i
31582 signslema
33871 circlemeth
33950 gg-cmvth
35466 poimirlem32
36823 broucube
36825 rrnmet
37000 eqrabdioph
41817 pellexlem1
41869 sineq0ALT
44000 digexp
47380 eenglngeehlnmlem2
47511 2itscp
47554 |