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Mirrors > Home > ILE Home > Th. List > 1nn0 | GIF version |
Description: 1 is a nonnegative integer. (Contributed by Raph Levien, 10-Dec-2002.) |
Ref | Expression |
---|---|
1nn0 | ⊢ 1 ∈ ℕ0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1nn 8844 | . 2 ⊢ 1 ∈ ℕ | |
2 | 1 | nnnn0i 9098 | 1 ⊢ 1 ∈ ℕ0 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2128 1c1 7733 ℕ0cn0 9090 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 ax-1re 7826 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-int 3808 df-inn 8834 df-n0 9091 |
This theorem is referenced by: peano2nn0 9130 deccl 9309 10nn0 9312 numsucc 9334 numadd 9341 numaddc 9342 11multnc 9362 6p5lem 9364 6p6e12 9368 7p5e12 9371 8p4e12 9376 9p2e11 9381 9p3e12 9382 10p10e20 9389 4t4e16 9393 5t2e10 9394 5t4e20 9396 6t3e18 9399 6t4e24 9400 7t3e21 9404 7t4e28 9405 8t3e24 9410 9t3e27 9417 9t9e81 9423 nn01to3 9526 elfzom1elp1fzo 10101 fzo0sn0fzo1 10120 1tonninf 10339 expn1ap0 10429 nn0expcl 10433 sqval 10477 sq10 10586 nn0opthlem1d 10594 fac2 10605 bccl 10641 hashsng 10672 1elfz0hash 10680 bcxmas 11386 arisum 11395 geoisum1 11416 geoisum1c 11417 cvgratnnlemsumlt 11425 mertenslem2 11433 fprodnn0cl 11509 ege2le3 11568 ef4p 11591 efgt1p2 11592 efgt1p 11593 sin01gt0 11658 dvds1 11744 3dvds2dec 11756 ennnfonelemhom 12144 dsndx 12348 dsid 12349 dsslid 12350 dveflem 13087 1kp2ke3k 13300 ex-exp 13303 ex-fac 13304 012of 13567 isomninnlem 13601 trilpolemisumle 13609 iswomninnlem 13620 iswomni0 13622 ismkvnnlem 13623 |
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