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Mirrors > Home > ILE Home > Th. List > 4nn0 | GIF version |
Description: 4 is a nonnegative integer. (Contributed by Mario Carneiro, 18-Feb-2014.) |
Ref | Expression |
---|---|
4nn0 | ⊢ 4 ∈ ℕ0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 4nn 9112 | . 2 ⊢ 4 ∈ ℕ | |
2 | 1 | nnnn0i 9214 | 1 ⊢ 4 ∈ ℕ0 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2160 4c4 9002 ℕ0cn0 9206 |
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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-sep 4136 ax-cnex 7932 ax-resscn 7933 ax-1re 7935 ax-addrcl 7938 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-int 3860 df-br 4019 df-iota 5196 df-fv 5243 df-ov 5899 df-inn 8950 df-2 9008 df-3 9009 df-4 9010 df-n0 9207 |
This theorem is referenced by: 6p5e11 9486 7p5e12 9490 8p5e13 9496 8p7e15 9498 9p5e14 9503 9p6e15 9504 4t3e12 9511 4t4e16 9512 5t5e25 9516 6t4e24 9519 6t5e30 9520 7t3e21 9523 7t5e35 9525 7t7e49 9527 8t3e24 9529 8t4e32 9530 8t5e40 9531 8t6e48 9532 8t7e56 9533 8t8e64 9534 9t5e45 9538 9t6e54 9539 9t7e63 9540 decbin3 9555 fzo0to42pr 10250 4bc3eq4 10785 resin4p 11758 recos4p 11759 ef01bndlem 11796 sin01bnd 11797 cos01bnd 11798 prm23lt5 12295 slotsdifdsndx 12732 slotsdifunifndx 12739 cnfldstr 13866 binom4 14857 ex-exp 14940 ex-fac 14941 ex-bc 14942 |
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