Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Union
The natural numbers (i.e., finite ordinals)
nnoni
Next ⟩
nnord
Metamath Proof Explorer
Ascii
Unicode
Theorem
nnoni
Description:
A natural number is an ordinal number.
(Contributed by
NM
, 27-Jun-1994)
Ref
Expression
Hypothesis
nnoni.1
⊢
A
∈
ω
Assertion
nnoni
⊢
A
∈
On
Proof
Step
Hyp
Ref
Expression
1
nnoni.1
⊢
A
∈
ω
2
nnon
⊢
A
∈
ω
→
A
∈
On
3
1
2
ax-mp
⊢
A
∈
On