Metamath Proof Explorer

Theorem fnom

Description: Functionality and domain of ordinal multiplication. (Contributed by NM, 26-Aug-1995) (Revised by Mario Carneiro, 8-Sep-2013)

Ref Expression
Assertion fnom ⊢⋅𝑜FnOn×On

Proof

Step Hyp Ref Expression
1 df-omul ⊢⋅𝑜=x∈On,y∈On⟼rec⁡z∈V⟼z+𝑜x∅⁡y
2 fvex ⊢rec⁡z∈V⟼z+𝑜x∅⁡y∈V
3 1 2 fnmpoi ⊢⋅𝑜FnOn×On