Colors of
variables: wff
setvar class |
Syntax hints: ¬ wn 3 → wi 4
↔ wb 205 ∧
wa 394 = wceq 1533
∈ wcel 2098 ≠
wne 2937 class class class wbr 5152
0cc0 11148 -∞cmnf 11286
ℝ*cxr 11287
< clt 11288 ≤
cle 11289 |
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 2699 ax-sep 5303 ax-nul 5310 ax-pow 5369 ax-pr 5433 ax-un 7748 ax-cnex 11204 ax-resscn 11205 ax-1cn 11206 ax-addrcl 11209 ax-rnegex 11219 ax-cnre 11221 ax-pre-lttri 11222 ax-pre-lttrn 11223 |
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 2529 df-eu 2558 df-clab 2706 df-cleq 2720 df-clel 2806 df-nfc 2881 df-ne 2938 df-nel 3044 df-ral 3059 df-rex 3068 df-rab 3431 df-v 3475 df-sbc 3779 df-csb 3895 df-dif 3952 df-un 3954 df-in 3956 df-ss 3966 df-nul 4327 df-if 4533 df-pw 4608 df-sn 4633 df-pr 4635 df-op 4639 df-uni 4913 df-br 5153 df-opab 5215 df-mpt 5236 df-id 5580 df-po 5594 df-so 5595 df-xp 5688 df-rel 5689 df-cnv 5690 df-co 5691 df-dm 5692 df-rn 5693 df-res 5694 df-ima 5695 df-iota 6505 df-fun 6555 df-fn 6556 df-f 6557 df-f1 6558 df-fo 6559 df-f1o 6560 df-fv 6561 df-er 8733 df-en 8973 df-dom 8974 df-sdom 8975 df-pnf 11290 df-mnf 11291 df-xr 11292 df-ltxr 11293 df-le 11294 |
This theorem is referenced by: xlesubadd
13284 xadddi2
13318 xrge0neqmnf
13471 xrge0subm
21354 isxmet2d
24261 xmetrtri
24289 imasdsf1olem
24307 xblpnfps
24329 xblpnf
24330 xblss2ps
24335 xblss2
24336 nmoix
24674 nmoleub
24676 blcvx
24742 xrge0gsumle
24777 xrge0tsms
24778 metdstri
24795 metdscnlem
24799 nmoleub2lem
25069 xrge0addass
32775 xrge0tsmsd
32800 |