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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 8853 | . 2 ⊢ 6 ∈ ℕ | |
2 | 1 | nnnn0i 8953 | 1 ⊢ 6 ∈ ℕ0 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1465 6c6 8743 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-4 8749 df-5 8750 df-6 8751 df-n0 8946 |
This theorem is referenced by: 6p5e11 9222 6p6e12 9223 7p7e14 9228 8p7e15 9234 9p7e16 9241 9p8e17 9242 6t3e18 9254 6t4e24 9255 6t5e30 9256 6t6e36 9257 7t7e49 9263 8t3e24 9265 8t7e56 9269 8t8e64 9270 9t4e36 9273 9t5e45 9274 9t7e63 9276 9t8e72 9277 6lcm4e12 11695 ex-exp 12866 |
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