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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 8579 | . 2 ⊢ 4 ∈ ℕ | |
2 | 1 | nnnn0i 8681 | 1 ⊢ 4 ∈ ℕ0 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1438 4c4 8475 ℕ0cn0 8673 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3957 ax-cnex 7436 ax-resscn 7437 ax-1re 7439 ax-addrcl 7442 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ral 2364 df-rex 2365 df-v 2621 df-un 3003 df-in 3005 df-ss 3012 df-sn 3452 df-pr 3453 df-op 3455 df-uni 3654 df-int 3689 df-br 3846 df-iota 4980 df-fv 5023 df-ov 5655 df-inn 8423 df-2 8481 df-3 8482 df-4 8483 df-n0 8674 |
This theorem is referenced by: 6p5e11 8949 7p5e12 8953 8p5e13 8959 8p7e15 8961 9p5e14 8966 9p6e15 8967 4t3e12 8974 4t4e16 8975 5t5e25 8979 6t4e24 8982 6t5e30 8983 7t3e21 8986 7t5e35 8988 7t7e49 8990 8t3e24 8992 8t4e32 8993 8t5e40 8994 8t6e48 8995 8t7e56 8996 8t8e64 8997 9t5e45 9001 9t6e54 9002 9t7e63 9003 decbin3 9018 fzo0to42pr 9631 4bc3eq4 10181 resin4p 11009 recos4p 11010 ef01bndlem 11047 sin01bnd 11048 cos01bnd 11049 ex-exp 11654 ex-fac 11655 ex-bc 11656 |
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