Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∈ wcel 2107
(class class class)co 7358 + caddc 11055 ℤcz 12500 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914
ax-6 1972 ax-7 2012 ax-8 2109
ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2708 ax-sep 5257 ax-nul 5264 ax-pow 5321 ax-pr 5385 ax-un 7673 ax-resscn 11109 ax-1cn 11110 ax-icn 11111 ax-addcl 11112 ax-addrcl 11113 ax-mulcl 11114 ax-mulrcl 11115 ax-mulcom 11116 ax-addass 11117 ax-mulass 11118 ax-distr 11119 ax-i2m1 11120 ax-1ne0 11121 ax-1rid 11122 ax-rnegex 11123 ax-rrecex 11124 ax-cnre 11125 ax-pre-lttri 11126 ax-pre-lttrn 11127 ax-pre-ltadd 11128 ax-pre-mulgt0 11129 |
This theorem depends on definitions:
df-bi 206 df-an 398
df-or 847 df-3or 1089 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2539 df-eu 2568 df-clab 2715 df-cleq 2729 df-clel 2815 df-nfc 2890 df-ne 2945 df-nel 3051 df-ral 3066 df-rex 3075 df-reu 3355 df-rab 3409 df-v 3448 df-sbc 3741 df-csb 3857 df-dif 3914 df-un 3916 df-in 3918 df-ss 3928 df-pss 3930 df-nul 4284 df-if 4488 df-pw 4563 df-sn 4588 df-pr 4590 df-op 4594 df-uni 4867 df-iun 4957 df-br 5107 df-opab 5169 df-mpt 5190 df-tr 5224 df-id 5532 df-eprel 5538 df-po 5546 df-so 5547 df-fr 5589 df-we 5591 df-xp 5640 df-rel 5641 df-cnv 5642 df-co 5643 df-dm 5644 df-rn 5645 df-res 5646 df-ima 5647 df-pred 6254 df-ord 6321 df-on 6322 df-lim 6323 df-suc 6324 df-iota 6449 df-fun 6499 df-fn 6500 df-f 6501 df-f1 6502 df-fo 6503 df-f1o 6504 df-fv 6505 df-riota 7314 df-ov 7361 df-oprab 7362 df-mpo 7363 df-om 7804 df-2nd 7923 df-frecs 8213 df-wrecs 8244 df-recs 8318 df-rdg 8357 df-er 8649 df-en 8885 df-dom 8886 df-sdom 8887 df-pnf 11192 df-mnf 11193 df-xr 11194 df-ltxr 11195 df-le 11196 df-sub 11388 df-neg 11389 df-nn 12155 df-n0 12415 df-z 12501 |
This theorem is referenced by: zadd2cl
12616 qaddcl
12891 elincfzoext
13631 eluzgtdifelfzo
13635 fladdz
13731 seqshft2
13935 expaddzlem
14012 sqoddm1div8
14147 ccatass
14477 cshf1
14699 2cshw
14702 2cshwcshw
14715 fsumrev2
15668 isumshft
15725 divcnvshft
15741 dvds2ln
16172 sadadd3
16342 sadaddlem
16347 sadadd
16348 bezoutlem4
16424 lcmgcdlem
16483 divgcdcoprm0
16542 hashdvds
16648 pythagtriplem4
16692 pythagtriplem11
16698 pcaddlem
16761 gzmulcl
16811 4sqlem8
16818 4sqlem10
16820 4sqlem11
16828 4sqlem14
16831 4sqlem16
16833 prmgaplem7
16930 prmgaplem8
16931 gsumsgrpccat
18651 mulgdir
18909 mndodconglem
19324 chfacfscmulfsupp
22211 chfacfpmmulfsupp
22215 ulmshftlem
25751 ulmshft
25752 dchrptlem2
26616 lgsqrlem2
26698 lgsquad2lem1
26735 2lgsoddprmlem2
26760 2sqlem4
26772 2sqlem8
26777 2sqmod
26787 crctcshwlkn0lem5
28762 numclwlk2lem2f
29324 ex-ind-dvds
29408 cshwrnid
31818 archirngz
32028 archiabllem2c
32034 qqhghm
32572 qqhrhm
32573 fsum2dsub
33223 breprexplemc
33248 divcnvlin
34308 caushft
36223 lcmineqlem22
40510 2np3bcnp1
40555 sticksstones7
40563 sticksstones10
40566 metakunt19
40598 metakunt21
40600 metakunt22
40601 metakunt25
40604 metakunt27
40606 metakunt29
40608 metakunt30
40609 metakunt32
40611 metakunt33
40612 prodsplit
40616 flt4lem3
40989 pell1234qrmulcl
41181 jm2.18
41315 jm2.19lem3
41318 jm2.19lem4
41319 jm2.25
41326 inductionexd
42434 fzisoeu
43541 uzubioo
43812 wallispilem4
44316 etransclem44
44526 gbowgt5
45961 mogoldbb
45984 nnsum4primesevenALTV
46000 2zlidl
46239 |