Metamath Proof Explorer


Theorem 7on

Description: Ordinal 7 is an ordinal number. (Contributed by BTernaryTau, 4-Sep-2026)

Ref Expression
Assertion 7on 7o ∈ On

Proof

Step Hyp Ref Expression
1 df-7o 7o = suc 6o
2 6on 6o ∈ On
3 2 onsuci suc 6o ∈ On
4 1 3 eqeltri 7o ∈ On