Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∧ w3a 1085
∈ wcel 2104 class class class wbr 5147
‘cfv 6542 (class class class)co 7411
≤ cle 11253 −
cmin 11448 ℕ0cn0 12476 ℤcz 12562 ℤ≥cuz 12826 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1911
ax-6 1969 ax-7 2009 ax-8 2106
ax-9 2114 ax-10 2135 ax-11 2152 ax-12 2169 ax-ext 2701 ax-sep 5298 ax-nul 5305 ax-pow 5362 ax-pr 5426 ax-un 7727 ax-cnex 11168 ax-resscn 11169 ax-1cn 11170 ax-icn 11171 ax-addcl 11172 ax-addrcl 11173 ax-mulcl 11174 ax-mulrcl 11175 ax-mulcom 11176 ax-addass 11177 ax-mulass 11178 ax-distr 11179 ax-i2m1 11180 ax-1ne0 11181 ax-1rid 11182 ax-rnegex 11183 ax-rrecex 11184 ax-cnre 11185 ax-pre-lttri 11186 ax-pre-lttrn 11187 ax-pre-ltadd 11188 ax-pre-mulgt0 11189 |
This theorem depends on definitions:
df-bi 206 df-an 395
df-or 844 df-3or 1086 df-3an 1087 df-tru 1542 df-fal 1552 df-ex 1780 df-nf 1784 df-sb 2066 df-mo 2532 df-eu 2561 df-clab 2708 df-cleq 2722 df-clel 2808 df-nfc 2883 df-ne 2939 df-nel 3045 df-ral 3060 df-rex 3069 df-reu 3375 df-rab 3431 df-v 3474 df-sbc 3777 df-csb 3893 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-pss 3966 df-nul 4322 df-if 4528 df-pw 4603 df-sn 4628 df-pr 4630 df-op 4634 df-uni 4908 df-iun 4998 df-br 5148 df-opab 5210 df-mpt 5231 df-tr 5265 df-id 5573 df-eprel 5579 df-po 5587 df-so 5588 df-fr 5630 df-we 5632 df-xp 5681 df-rel 5682 df-cnv 5683 df-co 5684 df-dm 5685 df-rn 5686 df-res 5687 df-ima 5688 df-pred 6299 df-ord 6366 df-on 6367 df-lim 6368 df-suc 6369 df-iota 6494 df-fun 6544 df-fn 6545 df-f 6546 df-f1 6547 df-fo 6548 df-f1o 6549 df-fv 6550 df-riota 7367 df-ov 7414 df-oprab 7415 df-mpo 7416 df-om 7858 df-2nd 7978 df-frecs 8268 df-wrecs 8299 df-recs 8373 df-rdg 8412 df-er 8705 df-en 8942 df-dom 8943 df-sdom 8944 df-pnf 11254 df-mnf 11255 df-xr 11256 df-ltxr 11257 df-le 11258 df-sub 11450 df-neg 11451 df-nn 12217 df-n0 12477 df-z 12563
df-uz 12827 |
This theorem is referenced by: fznn0sub
13537 elfzmlbm
13615 fzen2
13938 fzfi
13941 leexp2a
14141 hashfz
14391 ccatrn
14543 swrds2m
14896 isercoll2
15619 iseralt
15635 cvgrat
15833 fprodser
15897 dvdsexp
16275 bitsshft
16420 prmm2nn0
16639 hashdvds
16712 prmdiv
16722 prmdiveq
16723 pcaddlem
16825 vdwlem5
16922 vdwlem8
16925 dvn2bss
25680 aaliou3lem2
26092 lgsquadlem1
27119 crctcshwlkn0lem5
29335 clwwlknonex2lem1
29627 clwwlknonex2lem2
29628 numclwlk1lem2
29890 numclwwlk3lem1
29902 fiblem
33695 signstfveq0
33886 irrapxlem3
41864 itgsinexp
44969 wallispilem3
45081 fmtnorec3
46514 fmtnorec4
46515 |