Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∈ wcel 2107
(class class class)co 7358 1c1 11053
− cmin 11386 ℤcz 12500 |
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-resscn 11109 ax-1cn 11110 ax-icn 11111 ax-addcl 11112 ax-addrcl 11113 ax-mulcl 11114 ax-mulrcl 11115 ax-mulcom 11116 ax-addass 11117 ax-mulass 11118 ax-distr 11119 ax-i2m1 11120 ax-1ne0 11121 ax-1rid 11122 ax-rnegex 11123 ax-rrecex 11124 ax-cnre 11125 ax-pre-lttri 11126 ax-pre-lttrn 11127 ax-pre-ltadd 11128 ax-pre-mulgt0 11129 |
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-reu 3355 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-pss 3930 df-nul 4284 df-if 4488 df-pw 4563 df-sn 4588 df-pr 4590 df-op 4594 df-uni 4867 df-iun 4957 df-br 5107 df-opab 5169 df-mpt 5190 df-tr 5224 df-id 5532 df-eprel 5538 df-po 5546 df-so 5547 df-fr 5589 df-we 5591 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-pred 6254 df-ord 6321 df-on 6322 df-lim 6323 df-suc 6324 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-riota 7314 df-ov 7361 df-oprab 7362 df-mpo 7363 df-om 7804 df-2nd 7923 df-frecs 8213 df-wrecs 8244 df-recs 8318 df-rdg 8357 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 df-sub 11388 df-neg 11389 df-nn 12155 df-n0 12415 df-z 12501 |
This theorem is referenced by: zlem1lt
12556 zltlem1
12557 zextlt
12578 zeo
12590 eluzp1m1
12790 uzm1
12802 zbtwnre
12872 fz01en
13470 fzsuc2
13500 elfzm11
13513 uzdisj
13515 preduz
13564 predfz
13567 elfzo
13575 fzon
13594 fzoss2
13601 fzossrbm1
13602 fzosplitsnm1
13648 ubmelm1fzo
13669 elfzom1b
13672 fzosplitprm1
13683 fzoshftral
13690 sermono
13941 seqf1olem1
13948 seqf1olem2
13949 bcm1k
14216 bcn2
14220 bcp1m1
14221 bcpasc
14222 bccl
14223 hashbclem
14350 seqcoll
14364 revccat
14655 revrev
14656 absrdbnd
15227 fsumm1
15637 binomlem
15715 isumsplit
15726 climcndslem1
15735 arisum2
15747 pwdif
15754 pwm1geoser
15755 mertenslem1
15770 fprodser
15833 fprodm1
15851 risefacval2
15894 fallfacval2
15895 fallfacval3
15896 fallfacfwd
15920 binomfallfaclem2
15924 3dvds
16214 oddm1even
16226 oddp1even
16227 mod2eq1n2dvds
16230 zob
16242 nno
16265 pwp1fsum
16274 isprm3
16560 ncoprmlnprm
16604 hashdvds
16648 pockthlem
16778 4sqlem11
16828 vdwapun
16847 vdwnnlem2
16869 efgsp1
19520 efgsres
19521 srgbinomlem4
19961 srgbinomlem
19962 znunit
20973 dvexp3
25345 dvfsumlem1
25393 degltlem1
25440 atantayl2
26291 wilthlem1
26420 basellem5
26437 mersenne
26578 perfectlem1
26580 lgslem1
26648 lgsval2lem
26658 lgseisenlem1
26726 lgseisenlem2
26727 lgseisenlem3
26728 lgsquadlem1
26731 lgsquadlem3
26733 lgsquad2lem1
26735 lgsquad3
26738 2sqlem8
26777 2sqblem
26782 dchrisumlem1
26840 logdivbnd
26907 pntrsumbnd2
26918 ostth2lem3
26986 axlowdim
27913 pthdlem1
28717 pthdlem2
28719 wwlksm1edg
28829 clwwlkccatlem
28936 clwlkclwwlklem2fv1
28942 clwlkclwwlklem2a4
28944 clwlkclwwlklem2a
28945 clwlkclwwlklem2
28947 clwlkclwwlk
28949 clwwisshclwwslem
28961 clwwlkf
28994 wwlksubclwwlk
29005 numclwwlk5
29335 numclwwlk7
29338 frgrreggt1
29340 0nn0m1nnn0
33706 erdszelem7
33794 elfzm12
34266 fz0n
34306 fwddifnp1
34753 knoppndvlem2
34979 ltflcei
36069 poimirlem1
36082 poimirlem2
36083 poimirlem6
36087 poimirlem7
36088 poimirlem8
36089 poimirlem9
36090 poimirlem15
36096 poimirlem16
36097 poimirlem17
36098 poimirlem18
36099 poimirlem19
36100 poimirlem20
36101 poimirlem24
36105 poimirlem27
36108 poimirlem31
36112 poimirlem32
36113 mettrifi
36219 rmxluc
41263 rmyluc
41264 jm2.24
41290 jm2.18
41315 jm2.22
41322 jm2.23
41323 jm2.26lem3
41328 jm2.15nn0
41330 jm2.16nn0
41331 jm2.27a
41332 jm2.27c
41334 jm3.1lem3
41346 hashnzfz
42607 monoords
43538 fzisoeu
43541 dvnmul
44191 stoweidlem11
44259 dirkercncflem1
44351 fourierdlem48
44402 fourierdlem49
44403 fourierdlem65
44419 fourierdlem79
44433 zm1nn
45541 iccpartipre
45620 sfprmdvdsmersenne
45802 lighneallem4a
45807 proththd
45813 dfodd6
45836 evenm1odd
45838 oddm1eveni
45841 onego
45845 m1expoddALTV
45847 dfodd4
45858 oddflALTV
45862 oddm1evenALTV
45874 nnoALTV
45894 perfectALTVlem1
45920 altgsumbcALT
46436 pw2m1lepw2m1
46608 m1modmmod
46614 difmodm1lt
46615 zofldiv2
46624 logbpw2m1
46660 nnolog2flm1
46683 dignn0flhalflem1
46708 |