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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 8885 | . 2 ⊢ 6 ∈ ℕ | |
2 | 1 | nnnn0i 8985 | 1 ⊢ 6 ∈ ℕ0 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1480 6c6 8775 ℕ0cn0 8977 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-cnex 7711 ax-resscn 7712 ax-1re 7714 ax-addrcl 7717 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-int 3772 df-br 3930 df-iota 5088 df-fv 5131 df-ov 5777 df-inn 8721 df-2 8779 df-3 8780 df-4 8781 df-5 8782 df-6 8783 df-n0 8978 |
This theorem is referenced by: 6p5e11 9254 6p6e12 9255 7p7e14 9260 8p7e15 9266 9p7e16 9273 9p8e17 9274 6t3e18 9286 6t4e24 9287 6t5e30 9288 6t6e36 9289 7t7e49 9295 8t3e24 9297 8t7e56 9301 8t8e64 9302 9t4e36 9305 9t5e45 9306 9t7e63 9308 9t8e72 9309 6lcm4e12 11768 ex-exp 12939 |
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