Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∧ w3a 1087
∈ wcel 2106 class class class wbr 5148
‘cfv 6543 (class class class)co 7408
≤ cle 11248 −
cmin 11443 ℕ0cn0 12471 ℤcz 12557 ℤ≥cuz 12821 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913
ax-6 1971 ax-7 2011 ax-8 2108
ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2703 ax-sep 5299 ax-nul 5306 ax-pow 5363 ax-pr 5427 ax-un 7724 ax-cnex 11165 ax-resscn 11166 ax-1cn 11167 ax-icn 11168 ax-addcl 11169 ax-addrcl 11170 ax-mulcl 11171 ax-mulrcl 11172 ax-mulcom 11173 ax-addass 11174 ax-mulass 11175 ax-distr 11176 ax-i2m1 11177 ax-1ne0 11178 ax-1rid 11179 ax-rnegex 11180 ax-rrecex 11181 ax-cnre 11182 ax-pre-lttri 11183 ax-pre-lttrn 11184 ax-pre-ltadd 11185 ax-pre-mulgt0 11186 |
This theorem depends on definitions:
df-bi 206 df-an 397
df-or 846 df-3or 1088 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-mo 2534 df-eu 2563 df-clab 2710 df-cleq 2724 df-clel 2810 df-nfc 2885 df-ne 2941 df-nel 3047 df-ral 3062 df-rex 3071 df-reu 3377 df-rab 3433 df-v 3476 df-sbc 3778 df-csb 3894 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-pss 3967 df-nul 4323 df-if 4529 df-pw 4604 df-sn 4629 df-pr 4631 df-op 4635 df-uni 4909 df-iun 4999 df-br 5149 df-opab 5211 df-mpt 5232 df-tr 5266 df-id 5574 df-eprel 5580 df-po 5588 df-so 5589 df-fr 5631 df-we 5633 df-xp 5682 df-rel 5683 df-cnv 5684 df-co 5685 df-dm 5686 df-rn 5687 df-res 5688 df-ima 5689 df-pred 6300 df-ord 6367 df-on 6368 df-lim 6369 df-suc 6370 df-iota 6495 df-fun 6545 df-fn 6546 df-f 6547 df-f1 6548 df-fo 6549 df-f1o 6550 df-fv 6551 df-riota 7364 df-ov 7411 df-oprab 7412 df-mpo 7413 df-om 7855 df-2nd 7975 df-frecs 8265 df-wrecs 8296 df-recs 8370 df-rdg 8409 df-er 8702 df-en 8939 df-dom 8940 df-sdom 8941 df-pnf 11249 df-mnf 11250 df-xr 11251 df-ltxr 11252 df-le 11253 df-sub 11445 df-neg 11446 df-nn 12212 df-n0 12472 df-z 12558
df-uz 12822 |
This theorem is referenced by: fznn0sub
13532 elfzmlbm
13610 fzen2
13933 fzfi
13936 leexp2a
14136 hashfz
14386 ccatrn
14538 swrds2m
14891 isercoll2
15614 iseralt
15630 cvgrat
15828 fprodser
15892 dvdsexp
16270 bitsshft
16415 prmm2nn0
16634 hashdvds
16707 prmdiv
16717 prmdiveq
16718 pcaddlem
16820 vdwlem5
16917 vdwlem8
16920 dvn2bss
25446 aaliou3lem2
25855 lgsquadlem1
26880 crctcshwlkn0lem5
29065 clwwlknonex2lem1
29357 clwwlknonex2lem2
29358 numclwlk1lem2
29620 numclwwlk3lem1
29632 fiblem
33392 signstfveq0
33583 irrapxlem3
41552 itgsinexp
44661 wallispilem3
44773 fmtnorec3
46206 fmtnorec4
46207 |