Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Union
The natural numbers (i.e., finite ordinals)
nnon
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nnoni
Metamath Proof Explorer
Ascii
Unicode
Theorem
nnon
Description:
A natural number is an ordinal number.
(Contributed by
NM
, 27-Jun-1994)
Ref
Expression
Assertion
nnon
⊢
A
∈
ω
→
A
∈
On
Proof
Step
Hyp
Ref
Expression
1
omsson
⊢
ω
⊆
On
2
1
sseli
⊢
A
∈
ω
→
A
∈
On