Metamath Proof Explorer


Theorem mulsridd

Description: Surreal one is a right identity element for multiplication. (Contributed by Scott Fenton, 14-Mar-2025)

Ref Expression
Hypothesis mulsridd.1 ⊢ ( 𝜑 → 𝐴 ∈ No )
Assertion mulsridd ( 𝜑 → ( 𝐴 ·s 1s ) = 𝐴 )

Proof

Step Hyp Ref Expression
1 mulsridd.1 ⊢ ( 𝜑 → 𝐴 ∈ No )
2 mulsrid ⊢ ( 𝐴 ∈ No → ( 𝐴 ·s 1s ) = 𝐴 )
3 1 2 syl ⊢ ( 𝜑 → ( 𝐴 ·s 1s ) = 𝐴 )