Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∧ wa 395
∈ wcel 2098 class class class wbr 5139
(class class class)co 7402 ℝcr 11106
0cc0 11107 1c1 11108
+ caddc 11110 <
clt 11246 |
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 2695 ax-sep 5290 ax-nul 5297 ax-pow 5354 ax-pr 5418 ax-un 7719 ax-resscn 11164 ax-1cn 11165 ax-icn 11166 ax-addcl 11167 ax-addrcl 11168 ax-mulcl 11169 ax-mulrcl 11170 ax-mulcom 11171 ax-addass 11172 ax-mulass 11173 ax-distr 11174 ax-i2m1 11175 ax-1ne0 11176 ax-1rid 11177 ax-rnegex 11178 ax-rrecex 11179 ax-cnre 11180 ax-pre-lttri 11181 ax-pre-lttrn 11182 ax-pre-ltadd 11183 ax-pre-mulgt0 11184 |
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 2526 df-eu 2555 df-clab 2702 df-cleq 2716 df-clel 2802 df-nfc 2877 df-ne 2933 df-nel 3039 df-ral 3054 df-rex 3063 df-reu 3369 df-rab 3425 df-v 3468 df-sbc 3771 df-csb 3887 df-dif 3944 df-un 3946 df-in 3948 df-ss 3958 df-nul 4316 df-if 4522 df-pw 4597 df-sn 4622 df-pr 4624 df-op 4628 df-uni 4901 df-br 5140 df-opab 5202 df-mpt 5223 df-id 5565 df-po 5579 df-so 5580 df-xp 5673 df-rel 5674 df-cnv 5675 df-co 5676 df-dm 5677 df-rn 5678 df-res 5679 df-ima 5680 df-iota 6486 df-fun 6536 df-fn 6537 df-f 6538 df-f1 6539 df-fo 6540 df-f1o 6541 df-fv 6542 df-riota 7358 df-ov 7405 df-oprab 7406 df-mpo 7407 df-er 8700 df-en 8937 df-dom 8938 df-sdom 8939 df-pnf 11248 df-mnf 11249 df-xr 11250 df-ltxr 11251 df-le 11252 df-sub 11444 df-neg 11445 |
This theorem is referenced by: lep1
12053 letrp1
12056 recp1lt1
12110 ledivp1
12114 ltp1i
12116 ltp1d
12142 sup2
12168 uzind
12652 ge0p1rp
13003 qbtwnxr
13177 xrsupsslem
13284 supxrunb1
13296 fzp1disj
13558 fzneuz
13580 fzp1nel
13583 fsequb
13938 caubnd
15303 rlim2lt
15439 o1fsum
15757 pcprendvds
16774 pcmpt
16826 iocopnst
24788 bndth
24808 ovolicc2lem3
25372 ioorcl2
25425 itg2const2
25595 reeff1olem
26302 axlowdimlem13
28684 icoreunrn
36731 poimirlem4
36986 poimirlem22
37004 mblfinlem1
37019 aks4d1p1p4
41433 xrpnf
44706 limsupre3lem
44958 fourierdlem25
45358 smfresal
46014 natlocalincr
46100 |