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Mirrors > Home > ILE Home > Th. List > 7nn0 | GIF version |
Description: 7 is a nonnegative integer. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
7nn0 | ⊢ 7 ∈ ℕ0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 7nn 9004 | . 2 ⊢ 7 ∈ ℕ | |
2 | 1 | nnnn0i 9103 | 1 ⊢ 7 ∈ ℕ0 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2128 7c7 8894 ℕ0cn0 9095 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 ax-sep 4084 ax-cnex 7825 ax-resscn 7826 ax-1re 7828 ax-addrcl 7831 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-int 3810 df-br 3968 df-iota 5137 df-fv 5180 df-ov 5829 df-inn 8839 df-2 8897 df-3 8898 df-4 8899 df-5 8900 df-6 8901 df-7 8902 df-n0 9096 |
This theorem is referenced by: 7p4e11 9375 7p5e12 9376 7p6e13 9377 7p7e14 9378 8p8e16 9385 9p8e17 9392 9p9e18 9393 7t3e21 9409 7t4e28 9410 7t5e35 9411 7t6e42 9412 7t7e49 9413 8t8e64 9420 9t3e27 9422 9t4e36 9423 9t8e72 9427 9t9e81 9428 |
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