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Theorem prmssnn 11019
Description: The prime numbers are a subset of the positive integers. (Contributed by AV, 22-Jul-2020.)
Assertion
Ref Expression
prmssnn  |-  Prime  C_  NN

Proof of Theorem prmssnn
StepHypRef Expression
1 prmnn 11017 . 2  |-  ( x  e.  Prime  ->  x  e.  NN )
21ssriv 3018 1  |-  Prime  C_  NN
Colors of variables: wff set class
Syntax hints:    C_ wss 2988   NNcn 8360   Primecprime 11014
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-3an 924  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-ral 2360  df-rab 2364  df-v 2617  df-un 2992  df-in 2994  df-ss 3001  df-sn 3437  df-pr 3438  df-op 3440  df-br 3823  df-prm 11015
This theorem is referenced by:  prmex  11020
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