Theorem prmssnn 16636

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 16634	. 2 ⊢ (𝑥 ∈ ℙ → 𝑥 ∈ ℕ)
2	1	ssriv 3926	1 ⊢ ℙ ⊆ ℕ

Syntax hints:   ⊆ wss 3890  ℕcn 12165  ℙcprime 16631

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rab 3391  df-v 3432  df-dif 3893  df-un 3895  df-ss 3907  df-nul 4275  df-if 4468  df-sn 4569  df-pr 4571  df-op 4575  df-br 5087  df-prm 16632

This theorem is referenced by:  prmex  16637  prminf  16877  prmgaplem3  17015  prmgaplem4  17016  prmdvdsfi  27084  mumul  27158  sqff1o  27159  dirith2  27505  hgt750lema  34817  tgoldbachgtde  34820  tgoldbachgtda  34821  tgoldbachgt  34823  prmdvdsfmtnof1lem1  48059  prmdvdsfmtnof  48061