Colors of
variables: wff set class |
Syntax hints:
→ wi 4 ∈ wcel 2148
class class class wbr 4005 (class class class)co 5877
1c1 7814 ≤ cle 7995
ℕcn 8921 ℤcz 9255 ...cfz 10010 |
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-mpt 4068 df-id 4295 df-xp 4634 df-rel 4635 df-cnv 4636 df-co 4637 df-dm 4638 df-rn 4639 df-res 4640 df-ima 4641 df-iota 5180 df-fun 5220 df-fn 5221 df-f 5222 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 df-uz 9531 df-fz 10011 |
This theorem is referenced by: elfz1end
10057 fz1ssnn
10058 fzossnn
10191 bcm1k
10742 bcpasc
10748 seq3coll
10824 summodclem3
11390 summodclem2a
11391 fsum3
11397 isumz
11399 fsumcl2lem
11408 binomlem
11493 arisum2
11509 trireciplem
11510 geo2sum
11524 cvgratnnlemsumlt
11538 prodmodclem3
11585 prodmodclem2a
11586 fprodseq
11593 prod1dc
11596 fzm1ndvds
11864 nninfdcex
11956 nnmindc
12037 nnminle
12038 phicl
12217 eulerthlemrprm
12231 prmdivdiv
12239 phisum
12242 odzcllem
12244 odzdvds
12247 modprm0
12256 pcfac
12350 pcbc
12351 1arith
12367 mulgnn0z
13015 mulgnndir
13017 lgsval2lem
14450 lgseisenlem1
14489 lgseisenlem2
14490 cvgcmp2nlemabs
14819 trilpolemlt1
14828 nconstwlpolemgt0
14850 |