Theorem subsvald

Description: The value of surreal subtraction. (Contributed by Scott Fenton, 5-Feb-2025)

	Ref	Expression
Hypotheses	subsvald.1	$$⊢\phi \to A\in \mathrm{No}$$
	subsvald.2	$$⊢\phi \to B\in \mathrm{No}$$
Assertion	subsvald	$$⊢\phi \to A{-}_{s}B=A{+}_s{+}_s\left(B\right)$$

Proof

Step	Hyp	Ref	Expression
1		subsvald.1	$$⊢\phi \to A\in \mathrm{No}$$
2		subsvald.2	$$⊢\phi \to B\in \mathrm{No}$$
3		subsval	$$⊢\left(A\in \mathrm{No}\wedge B\in \mathrm{No}\right)\to A{-}_{s}B=A{+}_s{+}_s\left(B\right)$$
4	1 2 3	syl2anc	$$⊢\phi \to A{-}_{s}B=A{+}_s{+}_s\left(B\right)$$