Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∈ wcel 2106
(class class class)co 7411 ℝ*cxr 11251
+𝑒 cxad 13094 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913
ax-6 1971 ax-7 2011 ax-8 2108
ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2703 ax-sep 5299 ax-nul 5306 ax-pow 5363 ax-pr 5427 ax-un 7727 ax-cnex 11168 ax-1cn 11170 ax-addrcl 11173 ax-rnegex 11183 ax-cnre 11185 |
This theorem depends on definitions:
df-bi 206 df-an 397
df-or 846 df-3or 1088 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-mo 2534 df-eu 2563 df-clab 2710 df-cleq 2724 df-clel 2810 df-nfc 2885 df-ne 2941 df-ral 3062 df-rex 3071 df-rab 3433 df-v 3476 df-sbc 3778 df-csb 3894 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-nul 4323 df-if 4529 df-pw 4604 df-sn 4629 df-pr 4631 df-op 4635 df-uni 4909 df-iun 4999 df-br 5149 df-opab 5211 df-mpt 5232 df-id 5574 df-xp 5682 df-rel 5683 df-cnv 5684 df-co 5685 df-dm 5686 df-rn 5687 df-res 5688 df-ima 5689 df-iota 6495 df-fun 6545 df-fn 6546 df-f 6547 df-fv 6551 df-ov 7414 df-oprab 7415 df-mpo 7416 df-1st 7977 df-2nd 7978 df-pnf 11254 df-mnf 11255 df-xr 11256 df-xadd 13097 |
This theorem is referenced by: xadd4d
13286 imasdsf1olem
24099 bldisj
24124 xblss2ps
24127 xblss2
24128 blcld
24234 comet
24242 stdbdxmet
24244 metdstri
24587 metdscnlem
24591 iscau3
25019 xlt2addrd
32226 xrge0addcld
32230 xrge0subcld
32231 xrofsup
32235 xrsmulgzz
32434 xrge0adddir
32448 xrge0adddi
32449 esumle
33342 esumlef
33346 omssubadd
33585 inelcarsg
33596 carsgclctunlem2
33604 carsgclctunlem3
33605 carsgclctun
33606 xle2addd
44345 infrpge
44360 xrlexaddrp
44361 infleinflem1
44379 infleinflem2
44380 limsupgtlem
44792 ismbl3
45001 ismbl4
45008 sge0prle
45416 sge0split
45424 sge0iunmptlemre
45430 sge0xaddlem1
45448 omeunle
45531 carageniuncl
45538 ovnsubaddlem1
45585 hspmbl
45644 ovolval5lem1
45667 |