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Mirrors > Home > ILE Home > Th. List > 9nn0 | GIF version |
Description: 9 is a nonnegative integer. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
9nn0 | ⊢ 9 ∈ ℕ0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 9nn 9083 | . 2 ⊢ 9 ∈ ℕ | |
2 | 1 | nnnn0i 9180 | 1 ⊢ 9 ∈ ℕ0 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2148 9c9 8973 ℕ0cn0 9172 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 ax-sep 4120 ax-cnex 7899 ax-resscn 7900 ax-1re 7902 ax-addrcl 7905 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-int 3845 df-br 4003 df-iota 5177 df-fv 5223 df-ov 5875 df-inn 8916 df-2 8974 df-3 8975 df-4 8976 df-5 8977 df-6 8978 df-7 8979 df-8 8980 df-9 8981 df-n0 9173 |
This theorem is referenced by: deccl 9394 le9lt10 9406 decsucc 9420 9p2e11 9466 9p3e12 9467 9p4e13 9468 9p5e14 9469 9p6e15 9470 9p7e16 9471 9p8e17 9472 9p9e18 9473 9t3e27 9502 9t4e36 9503 9t5e45 9504 9t6e54 9505 9t7e63 9506 9t8e72 9507 9t9e81 9508 sq10e99m1 10686 3dvds2dec 11863 dsndxntsetndx 12667 unifndxntsetndx 12674 setsmsdsg 13851 |
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