Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∧ w3a 1086
∈ wcel 2105 class class class wbr 5149
‘cfv 6544 (class class class)co 7412
≤ cle 11254 −
cmin 11449 ℕ0cn0 12477 ℤcz 12563 ℤ≥cuz 12827 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912
ax-6 1970 ax-7 2010 ax-8 2107
ax-9 2115 ax-10 2136 ax-11 2153 ax-12 2170 ax-ext 2702 ax-sep 5300 ax-nul 5307 ax-pow 5364 ax-pr 5428 ax-un 7728 ax-cnex 11169 ax-resscn 11170 ax-1cn 11171 ax-icn 11172 ax-addcl 11173 ax-addrcl 11174 ax-mulcl 11175 ax-mulrcl 11176 ax-mulcom 11177 ax-addass 11178 ax-mulass 11179 ax-distr 11180 ax-i2m1 11181 ax-1ne0 11182 ax-1rid 11183 ax-rnegex 11184 ax-rrecex 11185 ax-cnre 11186 ax-pre-lttri 11187 ax-pre-lttrn 11188 ax-pre-ltadd 11189 ax-pre-mulgt0 11190 |
This theorem depends on definitions:
df-bi 206 df-an 396
df-or 845 df-3or 1087 df-3an 1088 df-tru 1543 df-fal 1553 df-ex 1781 df-nf 1785 df-sb 2067 df-mo 2533 df-eu 2562 df-clab 2709 df-cleq 2723 df-clel 2809 df-nfc 2884 df-ne 2940 df-nel 3046 df-ral 3061 df-rex 3070 df-reu 3376 df-rab 3432 df-v 3475 df-sbc 3779 df-csb 3895 df-dif 3952 df-un 3954 df-in 3956 df-ss 3966 df-pss 3968 df-nul 4324 df-if 4530 df-pw 4605 df-sn 4630 df-pr 4632 df-op 4636 df-uni 4910 df-iun 5000 df-br 5150 df-opab 5212 df-mpt 5233 df-tr 5267 df-id 5575 df-eprel 5581 df-po 5589 df-so 5590 df-fr 5632 df-we 5634 df-xp 5683 df-rel 5684 df-cnv 5685 df-co 5686 df-dm 5687 df-rn 5688 df-res 5689 df-ima 5690 df-pred 6301 df-ord 6368 df-on 6369 df-lim 6370 df-suc 6371 df-iota 6496 df-fun 6546 df-fn 6547 df-f 6548 df-f1 6549 df-fo 6550 df-f1o 6551 df-fv 6552 df-riota 7368 df-ov 7415 df-oprab 7416 df-mpo 7417 df-om 7859 df-2nd 7979 df-frecs 8269 df-wrecs 8300 df-recs 8374 df-rdg 8413 df-er 8706 df-en 8943 df-dom 8944 df-sdom 8945 df-pnf 11255 df-mnf 11256 df-xr 11257 df-ltxr 11258 df-le 11259 df-sub 11451 df-neg 11452 df-nn 12218 df-n0 12478 df-z 12564
df-uz 12828 |
This theorem is referenced by: fznn0sub
13538 elfzmlbm
13616 fzen2
13939 fzfi
13942 leexp2a
14142 hashfz
14392 ccatrn
14544 swrds2m
14897 isercoll2
15620 iseralt
15636 cvgrat
15834 fprodser
15898 dvdsexp
16276 bitsshft
16421 prmm2nn0
16640 hashdvds
16713 prmdiv
16723 prmdiveq
16724 pcaddlem
16826 vdwlem5
16923 vdwlem8
16926 dvn2bss
25680 aaliou3lem2
26089 lgsquadlem1
27116 crctcshwlkn0lem5
29332 clwwlknonex2lem1
29624 clwwlknonex2lem2
29625 numclwlk1lem2
29887 numclwwlk3lem1
29899 fiblem
33692 signstfveq0
33883 irrapxlem3
41865 itgsinexp
44971 wallispilem3
45083 fmtnorec3
46516 fmtnorec4
46517 |