Theorem prmssnn 12130

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

Step	Hyp	Ref	Expression
1		prmnn 12128	. 2 |- ( x e. Prime -> x e. NN )
2	1	ssriv 3174	1 |- Prime C_ NN

Syntax hints:   C_ wss 3144   NNcn 8937   Primecprime 12125

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

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-rab 2477  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-sn 3613  df-pr 3614  df-op 3616  df-br 4019  df-prm 12126

This theorem is referenced by:  prmex  12131  1arith  12383  prminf  12474