Theorem prmssnn 16700

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 16698	. 2 ⊢ (𝑥 ∈ ℙ → 𝑥 ∈ ℕ)
2	1	ssriv 3967	1 ⊢ ℙ ⊆ ℕ

Syntax hints:   ⊆ wss 3931  ℕcn 12245  ℙcprime 16695

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2715  df-cleq 2728  df-clel 2810  df-rab 3421  df-v 3466  df-dif 3934  df-un 3936  df-ss 3948  df-nul 4314  df-if 4506  df-sn 4607  df-pr 4609  df-op 4613  df-br 5125  df-prm 16696

This theorem is referenced by:  prmex  16701  prminf  16940  prmgaplem3  17078  prmgaplem4  17079  prmdvdsfi  27074  mumul  27148  sqff1o  27149  dirith2  27496  hgt750lema  34694  tgoldbachgtde  34697  tgoldbachgtda  34698  tgoldbachgt  34700  prmdvdsfmtnof1lem1  47565  prmdvdsfmtnof  47567