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Theorem piord 10918
Description: A positive integer is ordinal. (Contributed by NM, 29-Jan-1996.) (New usage is discouraged.)
Assertion
Ref Expression
piord (𝐴N → Ord 𝐴)

Proof of Theorem piord
StepHypRef Expression
1 pinn 10916 . 2 (𝐴N𝐴 ∈ ω)
2 nnord 7895 . 2 (𝐴 ∈ ω → Ord 𝐴)
31, 2syl 17 1 (𝐴N → Ord 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  Ord word 6385  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-ral 3060  df-rab 3434  df-v 3480  df-dif 3966  df-ss 3980  df-uni 4913  df-tr 5266  df-po 5597  df-so 5598  df-fr 5641  df-we 5643  df-ord 6389  df-on 6390  df-om 7888  df-ni 10910
This theorem is referenced by: (None)
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