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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 8944 |
. 2
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2 | nn0nnaddcl 9221 |
. 2
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3 | 1, 2 | mpan2 425 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
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 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 ax-sep 4133 ax-cnex 7916 ax-resscn 7917 ax-1cn 7918 ax-1re 7919 ax-icn 7920 ax-addcl 7921 ax-addrcl 7922 ax-mulcl 7923 ax-addcom 7925 ax-addass 7927 ax-i2m1 7930 ax-0id 7933 ax-rnegex 7934 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ral 2470 df-rex 2471 df-rab 2474 df-v 2751 df-un 3145 df-in 3147 df-ss 3154 df-sn 3610 df-pr 3611 df-op 3613 df-uni 3822 df-int 3857 df-br 4016 df-iota 5190 df-fv 5236 df-ov 5891 df-inn 8934 df-n0 9191 |
This theorem is referenced by: elnn0nn 9232 elz2 9338 peano5uzti 9375 fseq1p1m1 10108 fzonn0p1 10225 nn0ennn 10447 faccl 10729 facdiv 10732 facwordi 10734 faclbnd 10735 facubnd 10739 bcm1k 10754 bcp1n 10755 bcp1nk 10756 bcpasc 10760 bcxmas 11511 efcllemp 11680 uzwodc 12052 prmfac1 12166 pcfac 12362 |
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