Colors of
variables: wff set class |
Syntax hints: wn 3
wi 4
wa 104
wb 105 wo 708 w3o 977 wceq 1353 wcel 2148 class class class wbr 4005
cr 7812
cc0 7813
clt 7994
cneg 8131
cn 8921
cz 9255 |
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 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4123 ax-pow 4176 ax-pr 4211 ax-un 4435 ax-setind 4538 ax-cnex 7904 ax-resscn 7905 ax-1cn 7906 ax-1re 7907 ax-icn 7908 ax-addcl 7909 ax-addrcl 7910 ax-mulcl 7911 ax-addcom 7913 ax-addass 7915 ax-distr 7917 ax-i2m1 7918 ax-0lt1 7919 ax-0id 7921 ax-rnegex 7922 ax-cnre 7924 ax-pre-ltirr 7925 ax-pre-ltwlin 7926 ax-pre-lttrn 7927 ax-pre-ltadd 7929 |
This theorem depends on definitions:
df-bi 117 df-3or 979 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-nel 2443 df-ral 2460 df-rex 2461 df-reu 2462 df-rab 2464 df-v 2741 df-sbc 2965 df-dif 3133 df-un 3135 df-in 3137 df-ss 3144 df-pw 3579 df-sn 3600 df-pr 3601 df-op 3603 df-uni 3812 df-int 3847 df-br 4006 df-opab 4067 df-id 4295 df-xp 4634 df-rel 4635 df-cnv 4636 df-co 4637 df-dm 4638 df-iota 5180 df-fun 5220 df-fv 5226 df-riota 5833 df-ov 5880 df-oprab 5881 df-mpo 5882 df-pnf 7996 df-mnf 7997 df-xr 7998 df-ltxr 7999 df-le 8000 df-sub 8132 df-neg 8133 df-inn 8922 df-z 9256 |
This theorem is referenced by: nnssz
9272 elnnz1
9278 znnsub
9306 nn0ge0div
9342 msqznn
9355 elpq
9650 elfz1b
10092 lbfzo0
10183 fzo1fzo0n0
10185 elfzo0z
10186 fzofzim
10190 elfzodifsumelfzo
10203 exp3val
10524 nnesq
10642 nnabscl
11111 cvgratnnlemabsle
11537 p1modz1
11803 nndivdvds
11805 zdvdsdc
11821 oddge22np1
11888 evennn2n
11890 nno
11913 nnoddm1d2
11917 divalglemex
11929 divalglemeuneg
11930 divalg
11931 ndvdsadd
11938 sqgcd
12032 qredeu
12099 prmind2
12122 sqrt2irrlem
12163 sqrt2irrap
12182 qgt0numnn
12201 oddprm
12261 pythagtriplem6
12272 pythagtriplem11
12276 pythagtriplem13
12278 pythagtriplem19
12284 pc2dvds
12331 pcadd
12341 mulgval
12991 mulgfng
12992 subgmulg
13053 lgseisenlem1
14489 2sqlem8
14509 |