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Mirrors > Home > MPE Home > Th. List > 9nn0 | Structured version Visualization version 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 11069 | . 2 ⊢ 9 ∈ ℕ | |
2 | 1 | nnnn0i 11177 | 1 ⊢ 9 ∈ ℕ0 |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1977 9c9 10954 ℕ0cn0 11169 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-8 1979 ax-9 1986 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 ax-sep 4709 ax-nul 4717 ax-pow 4769 ax-pr 4833 ax-un 6847 ax-1cn 9873 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-3or 1032 df-3an 1033 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-eu 2462 df-mo 2463 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-ne 2782 df-ral 2901 df-rex 2902 df-reu 2903 df-rab 2905 df-v 3175 df-sbc 3403 df-csb 3500 df-dif 3543 df-un 3545 df-in 3547 df-ss 3554 df-pss 3556 df-nul 3875 df-if 4037 df-pw 4110 df-sn 4126 df-pr 4128 df-tp 4130 df-op 4132 df-uni 4373 df-iun 4457 df-br 4584 df-opab 4644 df-mpt 4645 df-tr 4681 df-eprel 4949 df-id 4953 df-po 4959 df-so 4960 df-fr 4997 df-we 4999 df-xp 5044 df-rel 5045 df-cnv 5046 df-co 5047 df-dm 5048 df-rn 5049 df-res 5050 df-ima 5051 df-pred 5597 df-ord 5643 df-on 5644 df-lim 5645 df-suc 5646 df-iota 5768 df-fun 5806 df-fn 5807 df-f 5808 df-f1 5809 df-fo 5810 df-f1o 5811 df-fv 5812 df-ov 6552 df-om 6958 df-wrecs 7294 df-recs 7355 df-rdg 7393 df-nn 10898 df-2 10956 df-3 10957 df-4 10958 df-5 10959 df-6 10960 df-7 10961 df-8 10962 df-9 10963 df-n0 11170 |
This theorem is referenced by: deccl 11388 le9lt10 11405 declecOLD 11420 decsucc 11426 decsuccOLD 11427 9p2e11 11495 9p2e11OLD 11496 9p3e12 11497 9p4e13 11498 9p5e14 11499 9p6e15 11500 9p7e16 11501 9p8e17 11502 9p9e18 11503 9t3e27 11540 9t4e36 11541 9t5e45 11542 9t6e54 11543 9t7e63 11544 9t8e72 11545 9t9e81 11546 sq10e99m1 12911 sq10e99m1OLD 12914 3dvds2dec 14894 3dvds2decOLD 14895 2exp8 15634 19prm 15663 prmlem2 15665 37prm 15666 83prm 15668 139prm 15669 163prm 15670 317prm 15671 631prm 15672 1259lem1 15676 1259lem2 15677 1259lem3 15678 1259lem4 15679 1259lem5 15680 1259prm 15681 2503lem1 15682 2503lem2 15683 2503lem3 15684 2503prm 15685 4001lem1 15686 4001lem2 15687 4001lem3 15688 4001lem4 15689 tuslem 21881 setsmsds 22091 tnglem 22254 tngds 22262 log2ublem3 24475 log2ub 24476 bposlem8 24816 kur14lem8 30449 fmtno5lem1 40003 fmtno5lem3 40005 fmtno5lem4 40006 fmtno5 40007 257prm 40011 fmtno4prmfac 40022 fmtno4prmfac193 40023 fmtno4nprmfac193 40024 fmtno5fac 40032 139prmALT 40049 127prm 40053 m11nprm 40056 tgblthelfgott 40229 tgoldbachlt 40230 tgblthelfgottOLD 40236 tgoldbachltOLD 40237 |
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