Database
SUPPLEMENTARY MATERIAL (USERS' MATHBOXES)
Mathbox for BTernaryTau
ZF set theory
Ordinals 5 through 9
5on
Next ⟩
6on
Metamath Proof Explorer
Ascii
Structured
Theorem
5on
Description:
Ordinal 5 is an ordinal number.
(Contributed by
BTernaryTau
, 4-Sep-2026)
Ref
Expression
Assertion
5on
⊢
5
o
∈ On
Proof
Step
Hyp
Ref
Expression
1
df-5o
⊢
5
o
= suc 4
o
2
4on
⊢
4
o
∈ On
3
2
onsuci
⊢
suc 4
o
∈ On
4
1
3
eqeltri
⊢
5
o
∈ On