Colors of
variables: wff set class |
Syntax hints: wi 4
wb 105 wcel 2146 class class class wbr 3998
cr 7785
cc0 7786
clt 7966
cneg 8103 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709
ax-5 1445 ax-7 1446 ax-gen 1447 ax-ie1 1491 ax-ie2 1492 ax-8 1502 ax-10 1503 ax-11 1504 ax-i12 1505 ax-bndl 1507 ax-4 1508 ax-17 1524 ax-i9 1528 ax-ial 1532 ax-i5r 1533 ax-13 2148 ax-14 2149 ax-ext 2157 ax-sep 4116 ax-pow 4169 ax-pr 4203 ax-un 4427 ax-setind 4530 ax-cnex 7877 ax-resscn 7878 ax-1cn 7879 ax-1re 7880 ax-icn 7881 ax-addcl 7882 ax-addrcl 7883 ax-mulcl 7884 ax-addcom 7886 ax-addass 7888 ax-distr 7890 ax-i2m1 7891 ax-0id 7894 ax-rnegex 7895 ax-cnre 7897 ax-pre-ltadd 7902 |
This theorem depends on definitions:
df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1459 df-sb 1761 df-eu 2027 df-mo 2028 df-clab 2162 df-cleq 2168 df-clel 2171 df-nfc 2306 df-ne 2346 df-nel 2441 df-ral 2458 df-rex 2459 df-reu 2460 df-rab 2462 df-v 2737 df-sbc 2961 df-dif 3129 df-un 3131 df-in 3133 df-ss 3140 df-pw 3574 df-sn 3595 df-pr 3596 df-op 3598 df-uni 3806 df-br 3999 df-opab 4060 df-id 4287 df-xp 4626 df-rel 4627 df-cnv 4628 df-co 4629 df-dm 4630 df-iota 5170 df-fun 5210 df-fv 5216 df-riota 5821 df-ov 5868 df-oprab 5869 df-mpo 5870 df-pnf 7968 df-mnf 7969 df-ltxr 7971 df-sub 8104 df-neg 8105 |
This theorem is referenced by: reapmul1
8526 recgt0
8778 prodgt0
8780 prodge0
8782 elnn0z
9237 ztri3or0
9266 exp3val
10490 expnegap0
10496 resqrexlemgt0
10996 climge0
11300 zdvdsdc
11786 divalglemex
11893 divalglemeuneg
11894 mulgval
12845 mulgfng
12846 sincosq4sgn
13743 sinq34lt0t
13745 coseq0negpitopi
13750 lgsdilem
13921 |