Colors of
variables: wff
setvar class |
Syntax hints: ¬ wn 3 → wi 4
↔ wb 205 ∧
wa 397 = wceq 1542
∈ wcel 2107 ≠
wne 2944 class class class wbr 5106
0cc0 11052 -∞cmnf 11188
ℝ*cxr 11189
< clt 11190 ≤
cle 11191 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914
ax-6 1972 ax-7 2012 ax-8 2109
ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2708 ax-sep 5257 ax-nul 5264 ax-pow 5321 ax-pr 5385 ax-un 7673 ax-cnex 11108 ax-resscn 11109 ax-1cn 11110 ax-addrcl 11113 ax-rnegex 11123 ax-cnre 11125 ax-pre-lttri 11126 ax-pre-lttrn 11127 |
This theorem depends on definitions:
df-bi 206 df-an 398
df-or 847 df-3or 1089 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2539 df-eu 2568 df-clab 2715 df-cleq 2729 df-clel 2815 df-nfc 2890 df-ne 2945 df-nel 3051 df-ral 3066 df-rex 3075 df-rab 3409 df-v 3448 df-sbc 3741 df-csb 3857 df-dif 3914 df-un 3916 df-in 3918 df-ss 3928 df-nul 4284 df-if 4488 df-pw 4563 df-sn 4588 df-pr 4590 df-op 4594 df-uni 4867 df-br 5107 df-opab 5169 df-mpt 5190 df-id 5532 df-po 5546 df-so 5547 df-xp 5640 df-rel 5641 df-cnv 5642 df-co 5643 df-dm 5644 df-rn 5645 df-res 5646 df-ima 5647 df-iota 6449 df-fun 6499 df-fn 6500 df-f 6501 df-f1 6502 df-fo 6503 df-f1o 6504 df-fv 6505 df-er 8649 df-en 8885 df-dom 8886 df-sdom 8887 df-pnf 11192 df-mnf 11193 df-xr 11194 df-ltxr 11195 df-le 11196 |
This theorem is referenced by: xlesubadd
13183 xadddi2
13217 xrge0neqmnf
13370 xrge0subm
20841 isxmet2d
23683 xmetrtri
23711 imasdsf1olem
23729 xblpnfps
23751 xblpnf
23752 xblss2ps
23757 xblss2
23758 nmoix
24096 nmoleub
24098 blcvx
24164 xrge0gsumle
24199 xrge0tsms
24200 metdstri
24217 metdscnlem
24221 nmoleub2lem
24480 xrge0addass
31884 xrge0tsmsd
31902 |