Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Union
The natural numbers (i.e., finite ordinals)
nnord
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trom
Metamath Proof Explorer
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Theorem
nnord
Description:
A natural number is ordinal.
(Contributed by
NM
, 17-Oct-1995)
Ref
Expression
Assertion
nnord
ω
⊢
A
∈
ω
→
Ord
A
Proof
Step
Hyp
Ref
Expression
1
nnon
ω
⊢
A
∈
ω
→
A
∈
On
2
eloni
⊢
A
∈
On
→
Ord
A
3
1
2
syl
ω
⊢
A
∈
ω
→
Ord
A