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Mirrors > Home > ILE Home > Th. List > 6nn0 | GIF version |
Description: 6 is a nonnegative integer. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
6nn0 | ⊢ 6 ∈ ℕ0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 6nn 8081 | . 2 ⊢ 6 ∈ ℕ | |
2 | 1 | nnnn0i 8189 | 1 ⊢ 6 ∈ ℕ0 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1393 6c6 7968 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-3 7974 df-4 7975 df-5 7976 df-6 7977 df-n0 8182 |
This theorem is referenced by: 6p5e11 8417 6p6e12 8418 7p7e14 8422 8p7e15 8427 9p7e16 8434 9p8e17 8435 6t3e18 8445 6t4e24 8446 6t5e30 8447 6t6e36 8448 7t7e49 8454 8t3e24 8456 8t7e56 8460 8t8e64 8461 9t4e36 8464 9t5e45 8465 9t7e63 8467 9t8e72 8468 |
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