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Theorem prmssnn 16713
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 16711 . 2 (𝑥 ∈ ℙ → 𝑥 ∈ ℕ)
21ssriv 3987 1 ℙ ⊆ ℕ
Colors of variables: wff setvar class
Syntax hints:  wss 3951  cn 12266  cprime 16708
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 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-br 5144  df-prm 16709
This theorem is referenced by:  prmex  16714  prminf  16953  prmgaplem3  17091  prmgaplem4  17092  prmdvdsfi  27150  mumul  27224  sqff1o  27225  dirith2  27572  hgt750lema  34672  tgoldbachgtde  34675  tgoldbachgtda  34676  tgoldbachgt  34678  prmdvdsfmtnof1lem1  47571  prmdvdsfmtnof  47573
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