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Theorem pion 10811
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 10810 . 2 (𝐴N𝐴 ∈ ω)
2 nnon 7804 . 2 (𝐴 ∈ ω → 𝐴 ∈ On)
31, 2syl 17 1 (𝐴N𝐴 ∈ On)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  Oncon0 6315  ωcom 7798  Ncnpi 10776
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-rab 3406  df-v 3445  df-dif 3911  df-in 3915  df-ss 3925  df-om 7799  df-ni 10804
This theorem is referenced by:  indpi  10839  nqereu  10861
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