Theorem negsval2d

Description: Surreal negation in terms of subtraction. (Contributed by Scott Fenton, 15-Apr-2025)

	Ref	Expression
Hypothesis	negsval2d.1	⊢ ( 𝜑 → 𝐴 ∈ No )
Assertion	negsval2d	⊢ ( 𝜑 → ( -us ‘ 𝐴 ) = ( 0s -s 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		negsval2d.1	⊢ ( 𝜑 → 𝐴 ∈ No )
2		negsval2	⊢ ( 𝐴 ∈ No → ( -us ‘ 𝐴 ) = ( 0s -s 𝐴 ) )
3	1 2	syl	⊢ ( 𝜑 → ( -us ‘ 𝐴 ) = ( 0s -s 𝐴 ) )