Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ↔ wb 205
∈ wcel 2098 class class class wbr 5143
(class class class)co 7416 ℝcr 11137
+ caddc 11141 <
clt 11278 − cmin 11474 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905
ax-6 1963 ax-7 2003 ax-8 2100
ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2166 ax-ext 2696 ax-sep 5294 ax-nul 5301 ax-pow 5359 ax-pr 5423 ax-un 7738 ax-resscn 11195 ax-1cn 11196 ax-icn 11197 ax-addcl 11198 ax-addrcl 11199 ax-mulcl 11200 ax-mulrcl 11201 ax-mulcom 11202 ax-addass 11203 ax-mulass 11204 ax-distr 11205 ax-i2m1 11206 ax-1ne0 11207 ax-1rid 11208 ax-rnegex 11209 ax-rrecex 11210 ax-cnre 11211 ax-pre-lttri 11212 ax-pre-lttrn 11213 ax-pre-ltadd 11214 |
This theorem depends on definitions:
df-bi 206 df-an 395
df-or 846 df-3or 1085 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2528 df-eu 2557 df-clab 2703 df-cleq 2717 df-clel 2802 df-nfc 2877 df-ne 2931 df-nel 3037 df-ral 3052 df-rex 3061 df-reu 3365 df-rab 3420 df-v 3465 df-sbc 3769 df-csb 3885 df-dif 3942 df-un 3944 df-in 3946 df-ss 3956 df-nul 4319 df-if 4525 df-pw 4600 df-sn 4625 df-pr 4627 df-op 4631 df-uni 4904 df-br 5144 df-opab 5206 df-mpt 5227 df-id 5570 df-po 5584 df-so 5585 df-xp 5678 df-rel 5679 df-cnv 5680 df-co 5681 df-dm 5682 df-rn 5683 df-res 5684 df-ima 5685 df-iota 6495 df-fun 6545 df-fn 6546 df-f 6547 df-f1 6548 df-fo 6549 df-f1o 6550 df-fv 6551 df-riota 7372 df-ov 7419 df-oprab 7420 df-mpo 7421 df-er 8723 df-en 8963 df-dom 8964 df-sdom 8965 df-pnf 11280 df-mnf 11281 df-ltxr 11283 df-sub 11476 df-neg 11477 |
This theorem is referenced by: subfzo0
13786 ccatrn
14571 cshwidxmod
14785 mulcn2
15572 reccn2
15573 rlimo1
15593 nrginvrcnlem
24626 ivthlem2
25399 itg2cnlem2
25710 dvferm1lem
25934 dvcvx
25971 ply1divex
26090 cxpcn3lem
26700 atantan
26873 lgamucov
26988 lgsquadlem2
27332 posbezout
41627 liminflimsupclim
45258 ioodvbdlimc1lem2
45383 fourierdlem82
45639 ioorrnopnlem
45755 sge0gtfsumgt
45894 smflimlem4
46225 ltsubsubb
47695 nnpw2pmod
47768 |