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Theorem pion 10917
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 10916 . 2 (𝐴N𝐴 ∈ ω)
2 nnon 7893 . 2 (𝐴 ∈ ω → 𝐴 ∈ On)
31, 2syl 17 1 (𝐴N𝐴 ∈ On)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  Oncon0 6386  ωcom 7887  Ncnpi 10882
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-rab 3434  df-v 3480  df-dif 3966  df-ss 3980  df-om 7888  df-ni 10910
This theorem is referenced by:  indpi  10945  nqereu  10967
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