| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 ∈ wcel 2098
(class class class)co 7404 1c1 11110
+ caddc 11112 ℤcz 12559 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905
ax-6 1963 ax-7 2003 ax-8 2100
ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2163 ax-ext 2697 ax-sep 5292 ax-nul 5299 ax-pow 5356 ax-pr 5420 ax-un 7721 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 396
df-or 845 df-3or 1085 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-mo 2528 df-eu 2557 df-clab 2704 df-cleq 2718 df-clel 2804 df-nfc 2879 df-ne 2935 df-nel 3041 df-ral 3056 df-rex 3065 df-reu 3371 df-rab 3427 df-v 3470 df-sbc 3773 df-csb 3889 df-dif 3946 df-un 3948 df-in 3950 df-ss 3960 df-pss 3962 df-nul 4318 df-if 4524 df-pw 4599 df-sn 4624 df-pr 4626 df-op 4630 df-uni 4903 df-iun 4992 df-br 5142 df-opab 5204 df-mpt 5225 df-tr 5259 df-id 5567 df-eprel 5573 df-po 5581 df-so 5582 df-fr 5624 df-we 5626 df-xp 5675 df-rel 5676 df-cnv 5677 df-co 5678 df-dm 5679 df-rn 5680 df-res 5681 df-ima 5682 df-pred 6293 df-ord 6360 df-on 6361 df-lim 6362 df-suc 6363 df-iota 6488 df-fun 6538 df-fn 6539 df-f 6540 df-f1 6541 df-fo 6542 df-f1o 6543 df-fv 6544 df-riota 7360 df-ov 7407 df-oprab 7408 df-mpo 7409 df-om 7852 df-2nd 7972 df-frecs 8264 df-wrecs 8295 df-recs 8369 df-rdg 8408 df-er 8702 df-en 8939 df-dom 8940 df-sdom 8941 df-pnf 11251 df-mnf 11252 df-xr 11253 df-ltxr 11254 df-le 11255 df-sub 11447 df-neg 11448 df-nn 12214 df-n0 12474 df-z 12560 |
| This theorem is referenced by: zleltp1
12614 btwnnz
12639 peano2uz2
12651 uzind
12655 uzind2
12656 peano2zd
12670 eluzp1m1
12849 eluzp1p1
12851 peano2uz
12886 zltaddlt1le
13485 elfzp1b
13581 fzval3
13704 fzossfzop1
13713 zesq
14191 hashfzp1
14393 odd2np1lem
16287 odd2np1
16288 mulsucdiv2z
16300 oddp1d2
16305 zob
16306 ltoddhalfle
16308 fldivp1
16836 telgsumfzs
19906 degltp1le
25959 ppiprm
27033 ppinprm
27034 chtprm
27035 chtnprm
27036 chtub
27095 lgsdir2lem2
27209 poimirlem3
37003 poimirlem4
37004 poimirlem16
37016 poimirlem17
37017 poimirlem19
37019 poimirlem20
37020 itg2addnclem2
37052 fdc
37125 ellz1
42065 rmxluc
42235 rmyluc
42236 jm2.27dlem2
42309 fzopredsuc
46585 icceuelpartlem
46657 oddp1evenALTV
46898 elfzolborelfzop1
47457 dignn0flhalflem1
47558 |
