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Mirrors > Home > ILE Home > Th. List > 3nn0 | GIF version |
Description: 3 is a nonnegative integer. (Contributed by Mario Carneiro, 18-Feb-2014.) |
Ref | Expression |
---|---|
3nn0 | ⊢ 3 ∈ ℕ0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3nn 9067 | . 2 ⊢ 3 ∈ ℕ | |
2 | 1 | nnnn0i 9170 | 1 ⊢ 3 ∈ ℕ0 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2148 3c3 8957 ℕ0cn0 9162 |
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 4118 ax-cnex 7890 ax-resscn 7891 ax-1re 7893 ax-addrcl 7896 |
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 3597 df-pr 3598 df-op 3600 df-uni 3808 df-int 3843 df-br 4001 df-iota 5174 df-fv 5220 df-ov 5872 df-inn 8906 df-2 8964 df-3 8965 df-n0 9163 |
This theorem is referenced by: 7p4e11 9445 7p7e14 9448 8p4e12 9451 8p6e14 9453 9p4e13 9458 9p5e14 9459 4t4e16 9468 5t4e20 9471 6t4e24 9475 6t6e36 9477 7t4e28 9480 7t6e42 9482 8t4e32 9486 8t5e40 9487 9t4e36 9493 9t5e45 9494 9t7e63 9496 9t8e72 9497 fz0to3un2pr 10106 4fvwrd4 10123 fldiv4p1lem1div2 10288 expnass 10608 binom3 10620 fac4 10694 4bc2eq6 10735 ef4p 11683 efi4p 11706 resin4p 11707 recos4p 11708 ef01bndlem 11745 sin01bnd 11746 sin01gt0 11750 dsndxnmulrndx 12629 tangtx 13919 binom4 14057 |
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