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Mirrors > Home > ILE Home > Th. List > nn0p1nn | Unicode version |
Description: A nonnegative integer plus 1 is a positive integer. (Contributed by Raph Levien, 30-Jun-2006.) (Revised by Mario Carneiro, 16-May-2014.) |
Ref | Expression |
---|---|
nn0p1nn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1nn 8589 |
. 2
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2 | nn0nnaddcl 8860 |
. 2
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3 | 1, 2 | mpan2 419 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-sep 3986 ax-cnex 7586 ax-resscn 7587 ax-1cn 7588 ax-1re 7589 ax-icn 7590 ax-addcl 7591 ax-addrcl 7592 ax-mulcl 7593 ax-addcom 7595 ax-addass 7597 ax-i2m1 7600 ax-0id 7603 ax-rnegex 7604 |
This theorem depends on definitions: df-bi 116 df-3an 932 df-tru 1302 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ral 2380 df-rex 2381 df-rab 2384 df-v 2643 df-un 3025 df-in 3027 df-ss 3034 df-sn 3480 df-pr 3481 df-op 3483 df-uni 3684 df-int 3719 df-br 3876 df-iota 5024 df-fv 5067 df-ov 5709 df-inn 8579 df-n0 8830 |
This theorem is referenced by: elnn0nn 8871 elz2 8974 peano5uzti 9011 fseq1p1m1 9715 fzonn0p1 9829 nn0ennn 10047 faccl 10322 facdiv 10325 facwordi 10327 faclbnd 10328 facubnd 10332 bcm1k 10347 bcp1n 10348 bcp1nk 10349 bcpasc 10353 bcxmas 11097 efcllemp 11162 prmfac1 11623 |
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