Theorem mulslidd

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

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

Proof

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