Database
SUPPLEMENTARY MATERIAL (USERS' MATHBOXES)
Mathbox for BTernaryTau
ZF set theory
Ordinals 5 through 9
9on
Next ⟩
5onn
Metamath Proof Explorer
Ascii
Structured
Theorem
9on
Description:
Ordinal 9 is an ordinal number.
(Contributed by
BTernaryTau
, 4-Sep-2026)
Ref
Expression
Assertion
9on
⊢
9
o
∈ On
Proof
Step
Hyp
Ref
Expression
1
df-9o
⊢
9
o
= suc 8
o
2
8on
⊢
8
o
∈ On
3
2
onsuci
⊢
suc 8
o
∈ On
4
1
3
eqeltri
⊢
9
o
∈ On