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Theorem pion 10922
Description: A positive integer is an ordinal number. (Contributed by NM, 23-Mar-1996.) (New usage is discouraged.)
Assertion
Ref Expression
pion (𝐴N𝐴 ∈ On)

Proof of Theorem pion
StepHypRef Expression
1 pinn 10921 . 2 (𝐴N𝐴 ∈ ω)
2 nnon 7882 . 2 (𝐴 ∈ ω → 𝐴 ∈ On)
31, 2syl 17 1 (𝐴N𝐴 ∈ On)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2099  Oncon0 6376  ωcom 7876  Ncnpi 10887
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2704  df-cleq 2718  df-clel 2803  df-rab 3420  df-v 3464  df-dif 3950  df-ss 3964  df-om 7877  df-ni 10915
This theorem is referenced by:  indpi  10950  nqereu  10972
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