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Theorem prmssnn 16018
 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
StepHypRef Expression
1 prmnn 16016 . 2 (𝑥 ∈ ℙ → 𝑥 ∈ ℕ)
21ssriv 3957 1 ℙ ⊆ ℕ
 Colors of variables: wff setvar class Syntax hints:   ⊆ wss 3919  ℕcn 11634  ℙcprime 16013 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 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-rab 3142  df-v 3482  df-un 3924  df-in 3926  df-ss 3936  df-sn 4551  df-pr 4553  df-op 4557  df-br 5053  df-prm 16014 This theorem is referenced by:  prmex  16019  prminf  16249  prmgaplem3  16387  prmgaplem4  16388  prmdvdsfi  25695  mumul  25769  sqff1o  25770  dirith2  26115  hgt750lema  31985  tgoldbachgtde  31988  tgoldbachgtda  31989  tgoldbachgt  31991  prmdvdsfmtnof1lem1  44027  prmdvdsfmtnof  44029
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