Theorem prmssnn 15390

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 15388	. 2 |- ( x e. Prime -> x e. NN )
2	1	ssriv 3607	1 |- Prime C_ NN

Syntax hints:   C_ wss 3574   NNcn 11020   Primecprime 15385

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1039  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ral 2917  df-rab 2921  df-v 3202  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-nul 3916  df-if 4087  df-sn 4178  df-pr 4180  df-op 4184  df-br 4654  df-prm 15386

This theorem is referenced by:  prmex  15391  prmgaplem3  15757  prmgaplem4  15758  hgt750lema  30735  tgoldbachgtde  30738  tgoldbachgtda  30739  tgoldbachgt  30741  prmdvdsfmtnof1lem1  41496  prmdvdsfmtnof  41498