Theorem prmssnn 16650

Description: The prime numbers are a subset of the positive integers. (Contributed by AV, 22-Jul-2020.)

Assertion

Ref	Expression
prmssnn	⊢ ℙ ⊆ ℕ

Proof of Theorem prmssnn

Step	Hyp	Ref	Expression
1		prmnn 16648	. 2 ⊢ (𝑥 ∈ ℙ → 𝑥 ∈ ℕ)
2	1	ssriv 3980	1 ⊢ ℙ ⊆ ℕ

Syntax hints:   ⊆ wss 3944  ℕcn 12245  ℙcprime 16645

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-rab 3419  df-v 3463  df-dif 3947  df-un 3949  df-ss 3961  df-nul 4323  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-br 5150  df-prm 16646

This theorem is referenced by:  prmex  16651  prminf  16887  prmgaplem3  17025  prmgaplem4  17026  prmdvdsfi  27084  mumul  27158  sqff1o  27159  dirith2  27506  hgt750lema  34420  tgoldbachgtde  34423  tgoldbachgtda  34424  tgoldbachgt  34426  prmdvdsfmtnof1lem1  47061  prmdvdsfmtnof  47063