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Theorem prmssnn 10874
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 10872 . 2  |-  ( x  e.  Prime  ->  x  e.  NN )
21ssriv 3014 1  |-  Prime  C_  NN
Colors of variables: wff set class
Syntax hints:    C_ wss 2984   NNcn 8316   Primecprime 10869
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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-rab 2362  df-v 2614  df-un 2988  df-in 2990  df-ss 2997  df-sn 3428  df-pr 3429  df-op 3431  df-br 3812  df-prm 10870
This theorem is referenced by:  prmex  10875
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