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Theorem nnoni 7895
Description: A natural number is an ordinal number. (Contributed by NM, 27-Jun-1994.)
Hypothesis
Ref Expression
nnoni.1 𝐴 ∈ ω
Assertion
Ref Expression
nnoni 𝐴 ∈ On

Proof of Theorem nnoni
StepHypRef Expression
1 nnoni.1 . 2 𝐴 ∈ ω
2 nnon 7894 . 2 (𝐴 ∈ ω → 𝐴 ∈ On)
31, 2ax-mp 5 1 𝐴 ∈ On
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  Oncon0 6383  ωcom 7888
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-rab 3436  df-ss 3967  df-om 7889
This theorem is referenced by:  omopthlem1  8698  omopthlem2  8699  omopthi  8700
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