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Theorem prmssnn 15769
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 15767 . 2 (𝑥 ∈ ℙ → 𝑥 ∈ ℕ)
21ssriv 3831 1 ℙ ⊆ ℕ
Colors of variables: wff setvar class
Syntax hints:  wss 3798  cn 11357  cprime 15764
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-10 2192  ax-11 2207  ax-12 2220  ax-13 2389  ax-ext 2803
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-3an 1113  df-tru 1660  df-ex 1879  df-nf 1883  df-sb 2068  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-ral 3122  df-rab 3126  df-v 3416  df-dif 3801  df-un 3803  df-in 3805  df-ss 3812  df-nul 4147  df-if 4309  df-sn 4400  df-pr 4402  df-op 4406  df-br 4876  df-prm 15765
This theorem is referenced by:  prmex  15770  prmgaplem3  16135  prmgaplem4  16136  hgt750lema  31280  tgoldbachgtde  31283  tgoldbachgtda  31284  tgoldbachgt  31286  prmdvdsfmtnof1lem1  42340  prmdvdsfmtnof  42342
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