Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∧ wa 397
∈ wcel 2107 ≠
wne 2944 class class class wbr 5110
ℝcr 11057 0cc0 11058
< clt 11196 |
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 5261 ax-nul 5268 ax-pow 5325 ax-pr 5389 ax-un 7677 ax-resscn 11115 ax-1cn 11116 ax-addrcl 11119 ax-rnegex 11129 ax-cnre 11131 ax-pre-lttri 11132 ax-pre-lttrn 11133 |
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 3411 df-v 3450 df-sbc 3745 df-csb 3861 df-dif 3918 df-un 3920 df-in 3922 df-ss 3932 df-nul 4288 df-if 4492 df-pw 4567 df-sn 4592 df-pr 4594 df-op 4598 df-uni 4871 df-br 5111 df-opab 5173 df-mpt 5194 df-id 5536 df-po 5550 df-so 5551 df-xp 5644 df-rel 5645 df-cnv 5646 df-co 5647 df-dm 5648 df-rn 5649 df-res 5650 df-ima 5651 df-iota 6453 df-fun 6503 df-fn 6504 df-f 6505 df-f1 6506 df-fo 6507 df-f1o 6508 df-fv 6509 df-er 8655 df-en 8891 df-dom 8892 df-sdom 8893 df-pnf 11198 df-mnf 11199 df-ltxr 11201 |
This theorem is referenced by: recgt0
12008 lemul1
12014 lediv1
12027 gt0div
12028 ge0div
12029 mulge0b
12032 ltdivmul
12037 ledivmul
12038 lt2mul2div
12040 lemuldiv
12042 ltdiv2
12048 ltrec1
12049 lerec2
12050 ledivdiv
12051 lediv2
12052 ltdiv23
12053 lediv23
12054 lediv12a
12055 recreclt
12061 nnrecl
12418 elnnz
12516 recnz
12585 rpne0
12938 divelunit
13418 resqrex
15142 sqrtgt0
15150 argregt0
25981 argimgt0
25983 logneg2
25986 logcnlem3
26015 atanlogsublem
26281 leopmul
31118 cdj1i
31417 lediv2aALT
34305 nndivlub
34959 knoppndvlem15
35018 knoppndvlem17
35020 sineq0ALT
43293 eenglngeehlnmlem1
46897 eenglngeehlnmlem2
46898 |