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Theorem nnoni 7814
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 7813 . 2 (𝐴 ∈ ω → 𝐴 ∈ On)
31, 2ax-mp 5 1 𝐴 ∈ On
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  Oncon0 6322  ωcom 7807
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-rab 3411  df-v 3450  df-in 3922  df-ss 3932  df-om 7808
This theorem is referenced by:  omopthlem1  8610  omopthlem2  8611  omopthi  8612
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