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Mirrors > Home > ILE Home > Th. List > 2z | GIF version |
Description: Two is an integer. (Contributed by NM, 10-May-2004.) |
Ref | Expression |
---|---|
2z | ⊢ 2 ∈ ℤ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2nn 8733 | . 2 ⊢ 2 ∈ ℕ | |
2 | 1 | nnzi 8927 | 1 ⊢ 2 ∈ ℤ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1448 2c2 8629 ℤcz 8906 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 584 ax-in2 585 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-13 1459 ax-14 1460 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-sep 3986 ax-pow 4038 ax-pr 4069 ax-un 4293 ax-setind 4390 ax-cnex 7586 ax-resscn 7587 ax-1cn 7588 ax-1re 7589 ax-icn 7590 ax-addcl 7591 ax-addrcl 7592 ax-mulcl 7593 ax-addcom 7595 ax-addass 7597 ax-distr 7599 ax-i2m1 7600 ax-0lt1 7601 ax-0id 7603 ax-rnegex 7604 ax-cnre 7606 ax-pre-ltirr 7607 ax-pre-ltwlin 7608 ax-pre-lttrn 7609 ax-pre-ltadd 7611 |
This theorem depends on definitions: df-bi 116 df-3or 931 df-3an 932 df-tru 1302 df-fal 1305 df-nf 1405 df-sb 1704 df-eu 1963 df-mo 1964 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ne 2268 df-nel 2363 df-ral 2380 df-rex 2381 df-reu 2382 df-rab 2384 df-v 2643 df-sbc 2863 df-dif 3023 df-un 3025 df-in 3027 df-ss 3034 df-pw 3459 df-sn 3480 df-pr 3481 df-op 3483 df-uni 3684 df-int 3719 df-br 3876 df-opab 3930 df-id 4153 df-xp 4483 df-rel 4484 df-cnv 4485 df-co 4486 df-dm 4487 df-iota 5024 df-fun 5061 df-fv 5067 df-riota 5662 df-ov 5709 df-oprab 5710 df-mpo 5711 df-pnf 7674 df-mnf 7675 df-xr 7676 df-ltxr 7677 df-le 7678 df-sub 7806 df-neg 7807 df-inn 8579 df-2 8637 df-z 8907 |
This theorem is referenced by: nn0n0n1ge2b 8982 nn0lt2 8984 nn0le2is012 8985 zadd2cl 9032 uzuzle23 9216 2eluzge1 9221 eluz2b1 9245 nn01to3 9259 nn0ge2m1nnALT 9260 ige2m1fz 9731 fzctr 9751 fzo0to2pr 9836 fzo0to42pr 9838 rebtwn2zlemshrink 9872 qbtwnre 9875 2tnp1ge0ge0 9915 flhalf 9916 m1modge3gt1 9985 q2txmodxeq0 9998 sq1 10227 expnass 10239 sqrecapd 10269 sqoddm1div8 10285 bcn2m1 10356 bcn2p1 10357 4bc2eq6 10361 resqrexlemcalc1 10626 resqrexlemnmsq 10629 resqrexlemcvg 10631 resqrexlemglsq 10634 resqrexlemga 10635 resqrexlemsqa 10636 efgt0 11188 tanval3ap 11219 cos01bnd 11263 cos01gt0 11267 egt2lt3 11281 zeo3 11360 odd2np1 11365 even2n 11366 oddm1even 11367 oddp1even 11368 oexpneg 11369 2tp1odd 11376 2teven 11379 evend2 11381 oddp1d2 11382 ltoddhalfle 11385 opoe 11387 omoe 11388 opeo 11389 omeo 11390 m1expo 11392 m1exp1 11393 nn0o1gt2 11397 nn0o 11399 z0even 11403 n2dvds1 11404 z2even 11406 n2dvds3 11407 z4even 11408 4dvdseven 11409 flodddiv4 11426 6gcd4e2 11476 3lcm2e6woprm 11560 isprm3 11592 prmind2 11594 dvdsnprmd 11599 prm2orodd 11600 2prm 11601 3prm 11602 oddprmge3 11608 divgcdodd 11614 pw2dvds 11636 sqrt2irraplemnn 11649 oddennn 11697 evenennn 11698 unennn 11702 exmidunben 11731 ex-fl 12540 ex-dvds 12545 cvgcmp2nlemabs 12811 trilpolemlt1 12818 |
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