Theorem prmssnn 16620

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 16618	. 2 ⊢ (𝑥 ∈ ℙ → 𝑥 ∈ ℕ)
2	1	ssriv 3986	1 ⊢ ℙ ⊆ ℕ

Syntax hints:   ⊆ wss 3948  ℕcn 12219  ℙcprime 16615

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2702

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2723  df-clel 2809  df-rab 3432  df-v 3475  df-dif 3951  df-un 3953  df-in 3955  df-ss 3965  df-nul 4323  df-if 4529  df-sn 4629  df-pr 4631  df-op 4635  df-br 5149  df-prm 16616

This theorem is referenced by:  prmex  16621  prminf  16855  prmgaplem3  16993  prmgaplem4  16994  prmdvdsfi  26953  mumul  27027  sqff1o  27028  dirith2  27375  hgt750lema  34134  tgoldbachgtde  34137  tgoldbachgtda  34138  tgoldbachgt  34140  prmdvdsfmtnof1lem1  46713  prmdvdsfmtnof  46715