Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ↔ wb 205
∈ wcel 2098 class class class wbr 5141
(class class class)co 7405 ℝcr 11111
+ caddc 11115 ≤
cle 11253 − cmin 11448 |
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 2163 ax-ext 2697 ax-sep 5292 ax-nul 5299 ax-pow 5356 ax-pr 5420 ax-un 7722 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 396
df-or 845 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 2704 df-cleq 2718 df-clel 2804 df-nfc 2879 df-ne 2935 df-nel 3041 df-ral 3056 df-rex 3065 df-reu 3371 df-rab 3427 df-v 3470 df-sbc 3773 df-csb 3889 df-dif 3946 df-un 3948 df-in 3950 df-ss 3960 df-nul 4318 df-if 4524 df-pw 4599 df-sn 4624 df-pr 4626 df-op 4630 df-uni 4903 df-br 5142 df-opab 5204 df-mpt 5225 df-id 5567 df-po 5581 df-so 5582 df-xp 5675 df-rel 5676 df-cnv 5677 df-co 5678 df-dm 5679 df-rn 5680 df-res 5681 df-ima 5682 df-iota 6489 df-fun 6539 df-fn 6540 df-f 6541 df-f1 6542 df-fo 6543 df-f1o 6544 df-fv 6545 df-riota 7361 df-ov 7408 df-oprab 7409 df-mpo 7410 df-er 8705 df-en 8942 df-dom 8943 df-sdom 8944 df-pnf 11254 df-mnf 11255 df-xr 11256 df-ltxr 11257 df-le 11258 df-sub 11450 df-neg 11451 |
This theorem is referenced by: elfzomelpfzo
13742 modaddmodup
13905 01sqrexlem7
15201 absrdbnd
15294 caucvgrlem
15625 cvgcmp
15768 oddge22np1
16299 ramub1lem1
16968 chfacfisf
22711 chfacfisfcpmat
22712 uniioombllem4
25470 mbfi1fseqlem6
25605 dvfsumlem1
25915 abelthlem2
26324 argimgt0
26501 harmonicbnd4
26898 ppiub
27092 logfaclbnd
27110 logfacbnd3
27111 bcmax
27166 lgseisen
27267 log2sumbnd
27432 chpdifbndlem1
27441 pntpbnd2
27475 pntibndlem2
27479 pntlemo
27495 crctcshwlkn0lem5
29577 clwlkclwwlklem2
29762 clwlkclwwlk2
29765 nvabs
30434 dnibndlem4
35865 dnibndlem10
35871 itg2addnclem2
37053 itg2addnclem3
37054 posbezout
41480 metakunt16
41561 fzmaxdif
42298 int-ineqmvtd
43519 binomcxplemnotnn0
43691 xrralrecnnge
44672 limsupgtlem
45065 fourierdlem26
45421 hoidmv1lelem1
45879 leaddsuble
46577 fmtnoge3
46770 fmtnoprmfac2lem1
46806 bgoldbtbndlem2
47046 nnolog2flm1
47551 |