Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 8197 | . 2 ⊢ 6 ∈ ℕ | |
2 | 1 | nnnn0i 8296 | 1 ⊢ 6 ∈ ℕ0 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1433 6c6 8093 ℕ0cn0 8288 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-cnex 7067 ax-resscn 7068 ax-1re 7070 ax-addrcl 7073 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-int 3637 df-br 3786 df-iota 4887 df-fv 4930 df-ov 5535 df-inn 8040 df-2 8098 df-3 8099 df-4 8100 df-5 8101 df-6 8102 df-n0 8289 |
This theorem is referenced by: 6p5e11 8549 6p6e12 8550 7p7e14 8555 8p7e15 8561 9p7e16 8568 9p8e17 8569 6t3e18 8581 6t4e24 8582 6t5e30 8583 6t6e36 8584 7t7e49 8590 8t3e24 8592 8t7e56 8596 8t8e64 8597 9t4e36 8600 9t5e45 8601 9t7e63 8603 9t8e72 8604 6lcm4e12 10469 |
Copyright terms: Public domain | W3C validator |