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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 8755 | . 2 ⊢ 1 ∈ ℕ | |
2 | 1 | nnnn0i 9009 | 1 ⊢ 1 ∈ ℕ0 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1481 1c1 7645 ℕ0cn0 9001 |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-1re 7738 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-int 3780 df-inn 8745 df-n0 9002 |
This theorem is referenced by: peano2nn0 9041 deccl 9220 10nn0 9223 numsucc 9245 numadd 9252 numaddc 9253 11multnc 9273 6p5lem 9275 6p6e12 9279 7p5e12 9282 8p4e12 9287 9p2e11 9292 9p3e12 9293 10p10e20 9300 4t4e16 9304 5t2e10 9305 5t4e20 9307 6t3e18 9310 6t4e24 9311 7t3e21 9315 7t4e28 9316 8t3e24 9321 9t3e27 9328 9t9e81 9334 nn01to3 9436 elfzom1elp1fzo 10010 fzo0sn0fzo1 10029 1tonninf 10244 expn1ap0 10334 nn0expcl 10338 sqval 10382 sq10 10490 nn0opthlem1d 10498 fac2 10509 bccl 10545 hashsng 10576 1elfz0hash 10584 bcxmas 11290 arisum 11299 geoisum1 11320 geoisum1c 11321 cvgratnnlemsumlt 11329 mertenslem2 11337 ege2le3 11414 ef4p 11437 efgt1p2 11438 efgt1p 11439 sin01gt0 11504 dvds1 11587 3dvds2dec 11599 ennnfonelemhom 11964 dsndx 12156 dsid 12157 dsslid 12158 dveflem 12895 1kp2ke3k 13107 ex-exp 13110 ex-fac 13111 012of 13363 isomninnlem 13400 trilpolemisumle 13406 iswomninnlem 13417 ismkvnnlem 13419 |
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