Colors of
variables: wff set class |
Syntax hints:
→ wi 4 ∈ wcel 2148
‘cfv 5217 (class class class)co 5875
ℤcz 9253 ℤ≥cuz 9528 ...cfz 10008 |
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 4122 ax-pow 4175 ax-pr 4210 ax-un 4434 ax-setind 4537 ax-cnex 7902 ax-resscn 7903 ax-pre-ltirr 7923 |
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-rab 2464 df-v 2740 df-sbc 2964 df-dif 3132 df-un 3134 df-in 3136 df-ss 3143 df-pw 3578 df-sn 3599 df-pr 3600 df-op 3602 df-uni 3811 df-br 4005 df-opab 4066 df-mpt 4067 df-id 4294 df-xp 4633 df-rel 4634 df-cnv 4635 df-co 4636 df-dm 4637 df-rn 4638 df-res 4639 df-ima 4640 df-iota 5179 df-fun 5219 df-fn 5220 df-f 5221 df-fv 5225 df-ov 5878 df-oprab 5879 df-mpo 5880 df-pnf 7994 df-mnf 7995 df-xr 7996 df-ltxr 7997 df-le 7998 df-neg 8131 df-z 9254 df-uz 9529 df-fz 10009 |
This theorem is referenced by: eluzfz2b
10033 elfzubelfz
10036 fzopth
10061 fzsuc
10069 fseq1p1m1
10094 fzm1
10100 fzneuz
10101 fzoend
10222 exfzdc
10240 uzsinds
10442 seq3clss
10467 seq3fveq2
10469 seq3shft2
10473 monoord
10476 monoord2
10477 seq3split
10479 seq3caopr3
10481 seq3f1olemp
10502 seq3id3
10507 seq3id2
10509 ser3ge0
10517 seq3coll
10822 summodclem2a
11389 fsumm1
11424 telfsumo
11474 telfsumo2
11475 fsumparts
11478 prodfap0
11553 prodfrecap
11554 prodmodclem2a
11584 fprodm1
11606 eulerthlemrprm
12229 eulerthlema
12230 nninfdclemlt
12452 supfz
14821 |