Metamath Proof Explorer


Theorem oa1cl

Description: A +o 1o is in On . (Contributed by RP, 27-Sep-2023)

Ref Expression
Assertion oa1cl ⊢ A ∈ On → A + 𝑜 1 𝑜 ∈ On

Proof

Step Hyp Ref Expression
1 1on ⊢ 1 𝑜 ∈ On
2 oacl ⊢ A ∈ On ∧ 1 𝑜 ∈ On → A + 𝑜 1 𝑜 ∈ On
3 1 2 mpan2 ⊢ A ∈ On → A + 𝑜 1 𝑜 ∈ On