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Mirrors > Home > ILE Home > Th. List > 2z | Unicode version |
Description: Two is an integer. (Contributed by NM, 10-May-2004.) |
Ref | Expression |
---|---|
2z |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2nn 8874 | . 2 | |
2 | 1 | nnzi 9068 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1480 c2 8764 cz 9047 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-un 4350 ax-setind 4447 ax-cnex 7704 ax-resscn 7705 ax-1cn 7706 ax-1re 7707 ax-icn 7708 ax-addcl 7709 ax-addrcl 7710 ax-mulcl 7711 ax-addcom 7713 ax-addass 7715 ax-distr 7717 ax-i2m1 7718 ax-0lt1 7719 ax-0id 7721 ax-rnegex 7722 ax-cnre 7724 ax-pre-ltirr 7725 ax-pre-ltwlin 7726 ax-pre-lttrn 7727 ax-pre-ltadd 7729 |
This theorem depends on definitions: df-bi 116 df-3or 963 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ne 2307 df-nel 2402 df-ral 2419 df-rex 2420 df-reu 2421 df-rab 2423 df-v 2683 df-sbc 2905 df-dif 3068 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-int 3767 df-br 3925 df-opab 3985 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-iota 5083 df-fun 5120 df-fv 5126 df-riota 5723 df-ov 5770 df-oprab 5771 df-mpo 5772 df-pnf 7795 df-mnf 7796 df-xr 7797 df-ltxr 7798 df-le 7799 df-sub 7928 df-neg 7929 df-inn 8714 df-2 8772 df-z 9048 |
This theorem is referenced by: nn0n0n1ge2b 9123 nn0lt2 9125 nn0le2is012 9126 zadd2cl 9173 uzuzle23 9359 2eluzge1 9364 eluz2b1 9388 nn01to3 9402 nn0ge2m1nnALT 9403 ige2m1fz 9883 fzctr 9903 fzo0to2pr 9988 fzo0to42pr 9990 qbtwnre 10027 2tnp1ge0ge0 10067 flhalf 10068 m1modge3gt1 10137 q2txmodxeq0 10150 sq1 10379 expnass 10391 sqrecapd 10421 sqoddm1div8 10437 bcn2m1 10508 bcn2p1 10509 4bc2eq6 10513 resqrexlemcalc1 10779 resqrexlemnmsq 10782 resqrexlemcvg 10784 resqrexlemglsq 10787 resqrexlemga 10788 resqrexlemsqa 10789 efgt0 11379 tanval3ap 11410 cos01bnd 11454 cos01gt0 11458 egt2lt3 11475 zeo3 11554 odd2np1 11559 even2n 11560 oddm1even 11561 oddp1even 11562 oexpneg 11563 2tp1odd 11570 2teven 11573 evend2 11575 oddp1d2 11576 ltoddhalfle 11579 opoe 11581 omoe 11582 opeo 11583 omeo 11584 m1expo 11586 m1exp1 11587 nn0o1gt2 11591 nn0o 11593 z0even 11597 n2dvds1 11598 z2even 11600 n2dvds3 11601 z4even 11602 4dvdseven 11603 flodddiv4 11620 6gcd4e2 11672 3lcm2e6woprm 11756 isprm3 11788 prmind2 11790 dvdsnprmd 11795 prm2orodd 11796 2prm 11797 3prm 11798 oddprmge3 11804 divgcdodd 11810 pw2dvds 11833 sqrt2irraplemnn 11846 oddennn 11894 evenennn 11895 unennn 11899 exmidunben 11928 sincos6thpi 12912 ex-fl 12926 ex-dvds 12931 cvgcmp2nlemabs 13216 trilpolemlt1 13223 |
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