Database
SUPPLEMENTARY MATERIAL (USERS' MATHBOXES)
Mathbox for BTernaryTau
ZF set theory
Ordinals 5 through 9
7on
Next ⟩
8on
Metamath Proof Explorer
Ascii
Structured
Theorem
7on
Description:
Ordinal 7 is an ordinal number.
(Contributed by
BTernaryTau
, 4-Sep-2026)
Ref
Expression
Assertion
7on
⊢
7
o
∈ On
Proof
Step
Hyp
Ref
Expression
1
df-7o
⊢
7
o
= suc 6
o
2
6on
⊢
6
o
∈ On
3
2
onsuci
⊢
suc 6
o
∈ On
4
1
3
eqeltri
⊢
7
o
∈ On