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Mirrors > Home > ILE Home > Th. List > 2nn0 | GIF version |
Description: 2 is a nonnegative integer. (Contributed by Raph Levien, 10-Dec-2002.) |
Ref | Expression |
---|---|
2nn0 | ⊢ 2 ∈ ℕ0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2nn 8849 | . 2 ⊢ 2 ∈ ℕ | |
2 | 1 | nnnn0i 8953 | 1 ⊢ 2 ∈ ℕ0 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1465 2c2 8739 ℕ0cn0 8945 |
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-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-cnex 7679 ax-resscn 7680 ax-1re 7682 ax-addrcl 7685 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-int 3742 df-br 3900 df-iota 5058 df-fv 5101 df-ov 5745 df-inn 8689 df-2 8747 df-n0 8946 |
This theorem is referenced by: nn0n0n1ge2 9089 7p6e13 9227 8p3e11 9230 8p5e13 9232 9p3e12 9237 9p4e13 9238 4t3e12 9247 4t4e16 9248 5t3e15 9250 5t5e25 9252 6t3e18 9254 6t5e30 9256 7t3e21 9259 7t4e28 9260 7t5e35 9261 7t6e42 9262 7t7e49 9263 8t3e24 9265 8t4e32 9266 8t5e40 9267 9t3e27 9272 9t4e36 9273 9t8e72 9277 9t9e81 9278 decbin3 9291 2eluzge0 9338 nn01to3 9377 xnn0le2is012 9617 fzo0to42pr 9965 nn0sqcl 10288 sqmul 10323 resqcl 10328 zsqcl 10331 cu2 10359 i3 10362 i4 10363 binom3 10377 nn0opthlem1d 10434 fac3 10446 faclbnd2 10456 abssq 10821 sqabs 10822 ef4p 11327 efgt1p2 11328 efi4p 11351 ef01bndlem 11390 cos01bnd 11392 oexpneg 11501 oddge22np1 11505 setsmsdsg 12576 dveflem 12782 tangtx 12846 1kp2ke3k 12863 ex-exp 12866 ex-fac 12867 |
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