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Mirrors > Home > ILE Home > Th. List > 3nn0 | GIF version |
Description: 3 is a nonnegative integer. (Contributed by Mario Carneiro, 18-Feb-2014.) |
Ref | Expression |
---|---|
3nn0 | ⊢ 3 ∈ ℕ0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3nn 8850 | . 2 ⊢ 3 ∈ ℕ | |
2 | 1 | nnnn0i 8953 | 1 ⊢ 3 ∈ ℕ0 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1465 3c3 8740 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-3 8748 df-n0 8946 |
This theorem is referenced by: 7p4e11 9225 7p7e14 9228 8p4e12 9231 8p6e14 9233 9p4e13 9238 9p5e14 9239 4t4e16 9248 5t4e20 9251 6t4e24 9255 6t6e36 9257 7t4e28 9260 7t6e42 9262 8t4e32 9266 8t5e40 9267 9t4e36 9273 9t5e45 9274 9t7e63 9276 9t8e72 9277 4fvwrd4 9885 fldiv4p1lem1div2 10046 expnass 10366 binom3 10377 fac4 10447 4bc2eq6 10488 ef4p 11327 efi4p 11351 resin4p 11352 recos4p 11353 ef01bndlem 11390 sin01bnd 11391 sin01gt0 11395 tangtx 12846 |
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