Theorem cutscld

Description: Closure law for surreal cuts. (Contributed by Scott Fenton, 23-Aug-2024)

	Ref	Expression
Hypothesis	cutscld.1	$$⊢\phi \to A{\ll }_{s}B$$
Assertion	cutscld	$$⊢\phi \to A{|}_{s}B\in \mathrm{No}$$

Proof

Step	Hyp	Ref	Expression
1		cutscld.1	$$⊢\phi \to A{\ll }_{s}B$$
2		cutscl	$$⊢A{\ll }_{s}B\to A{|}_{s}B\in \mathrm{No}$$
3	1 2	syl	$$⊢\phi \to A{|}_{s}B\in \mathrm{No}$$