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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 7855 | . 2 ⊢ 2 ∈ ℕ | |
2 | 1 | nnnn0i 7965 | 1 ⊢ 2 ∈ ℕ0 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1390 2c2 7744 ℕ0cn0 7957 |
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 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-sep 3866 ax-cnex 6774 ax-resscn 6775 ax-1re 6777 ax-addrcl 6780 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-ral 2305 df-rex 2306 df-v 2553 df-un 2916 df-in 2918 df-ss 2925 df-sn 3373 df-pr 3374 df-op 3376 df-uni 3572 df-int 3607 df-br 3756 df-iota 4810 df-fv 4853 df-ov 5458 df-inn 7696 df-2 7753 df-n0 7958 |
This theorem is referenced by: nn0n0n1ge2 8087 7p6e13 8197 8p3e11 8199 8p5e13 8201 9p3e12 8206 9p4e13 8207 4t3e12 8215 4t4e16 8216 5t3e15 8217 5t5e25 8219 6t3e18 8221 6t5e30 8223 7t3e21 8226 7t4e28 8227 7t5e35 8228 7t6e42 8229 7t7e49 8230 8t3e24 8232 8t4e32 8233 8t5e40 8234 9t3e27 8239 9t4e36 8240 9t8e72 8244 9t9e81 8245 decbin3 8248 2eluzge0 8293 nn01to3 8328 fzo0to42pr 8846 nn0sqcl 8936 sqmul 8970 resqcl 8974 zsqcl 8977 cu2 9004 i3 9007 i4 9008 binom3 9019 |
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