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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 8077 | . 2 ⊢ 2 ∈ ℕ | |
2 | 1 | nnnn0i 8189 | 1 ⊢ 2 ∈ ℕ0 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1393 2c2 7964 ℕ0cn0 8181 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-cnex 6975 ax-resscn 6976 ax-1re 6978 ax-addrcl 6981 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-int 3616 df-br 3765 df-iota 4867 df-fv 4910 df-ov 5515 df-inn 7915 df-2 7973 df-n0 8182 |
This theorem is referenced by: nn0n0n1ge2 8311 7p6e13 8421 8p3e11 8423 8p5e13 8425 9p3e12 8430 9p4e13 8431 4t3e12 8439 4t4e16 8440 5t3e15 8441 5t5e25 8443 6t3e18 8445 6t5e30 8447 7t3e21 8450 7t4e28 8451 7t5e35 8452 7t6e42 8453 7t7e49 8454 8t3e24 8456 8t4e32 8457 8t5e40 8458 9t3e27 8463 9t4e36 8464 9t8e72 8468 9t9e81 8469 decbin3 8472 2eluzge0 8517 nn01to3 8552 fzo0to42pr 9076 nn0sqcl 9282 sqmul 9316 resqcl 9321 zsqcl 9324 cu2 9351 i3 9354 i4 9355 binom3 9366 abssq 9677 sqabs 9678 |
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