Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Union
The natural numbers (i.e., finite ordinals)
nnon
Next ⟩
nnoni
Metamath Proof Explorer
Ascii
Structured
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 )