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Theorem prmssnn 16557
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 16555 . 2 (𝑥 ∈ ℙ → 𝑥 ∈ ℕ)
21ssriv 3949 1 ℙ ⊆ ℕ
Colors of variables: wff setvar class
Syntax hints:  wss 3911  cn 12158  cprime 16552
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3407  df-v 3446  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4284  df-if 4488  df-sn 4588  df-pr 4590  df-op 4594  df-br 5107  df-prm 16553
This theorem is referenced by:  prmex  16558  prminf  16792  prmgaplem3  16930  prmgaplem4  16931  prmdvdsfi  26472  mumul  26546  sqff1o  26547  dirith2  26892  hgt750lema  33327  tgoldbachgtde  33330  tgoldbachgtda  33331  tgoldbachgt  33333  prmdvdsfmtnof1lem1  45862  prmdvdsfmtnof  45864
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