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Mirrors > Home > ILE Home > Th. List > nn0nnaddcl | Unicode version |
Description: A nonnegative integer plus a positive integer is a positive integer. (Contributed by NM, 22-Dec-2005.) |
Ref | Expression |
---|---|
nn0nnaddcl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nncn 8957 |
. . . 4
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2 | nn0cn 9216 |
. . . 4
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3 | addcom 8124 |
. . . 4
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4 | 1, 2, 3 | syl2an 289 |
. . 3
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5 | nnnn0addcl 9236 |
. . 3
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6 | 4, 5 | eqeltrrd 2267 |
. 2
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7 | 6 | ancoms 268 |
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 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-sep 4136 ax-cnex 7932 ax-resscn 7933 ax-1cn 7934 ax-1re 7935 ax-icn 7936 ax-addcl 7937 ax-addrcl 7938 ax-mulcl 7939 ax-addcom 7941 ax-addass 7943 ax-i2m1 7946 ax-0id 7949 ax-rnegex 7950 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-rab 2477 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-int 3860 df-br 4019 df-iota 5196 df-fv 5243 df-ov 5899 df-inn 8950 df-n0 9207 |
This theorem is referenced by: nn0p1nn 9245 nnaddm1cl 9344 numnncl 9423 modfzo0difsn 10426 |
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