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Theorem prmssnn 15795
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 15793 . 2 (𝑥 ∈ ℙ → 𝑥 ∈ ℕ)
21ssriv 3825 1 ℙ ⊆ ℕ
Colors of variables: wff setvar class
Syntax hints:  wss 3792  cn 11374  cprime 15790
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-9 2116  ax-10 2135  ax-11 2150  ax-12 2163  ax-13 2334  ax-ext 2754
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-3an 1073  df-tru 1605  df-ex 1824  df-nf 1828  df-sb 2012  df-clab 2764  df-cleq 2770  df-clel 2774  df-nfc 2921  df-ral 3095  df-rab 3099  df-v 3400  df-dif 3795  df-un 3797  df-in 3799  df-ss 3806  df-nul 4142  df-if 4308  df-sn 4399  df-pr 4401  df-op 4405  df-br 4887  df-prm 15791
This theorem is referenced by:  prmex  15796  prminf  16023  prmgaplem3  16161  prmgaplem4  16162  hgt750lema  31337  tgoldbachgtde  31340  tgoldbachgtda  31341  tgoldbachgt  31343  prmdvdsfmtnof1lem1  42517  prmdvdsfmtnof  42519
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