Theorem sltmul2d

Description: Multiplication of both sides of surreal less-than by a positive number. (Contributed by Scott Fenton, 10-Mar-2025)

	Ref	Expression
Hypotheses	sltmul12d.1	$$⊢\phi \to A\in \mathrm{No}$$
	sltmul12d.2	$$⊢\phi \to B\in \mathrm{No}$$
	sltmul12d.3	$$⊢\phi \to C\in \mathrm{No}$$
	sltmul12d.4	No typesetting found for |- ( ph -> 0s
Assertion	sltmul2d	Could not format assertion : No typesetting found for |- ( ph -> ( A ( C x.s A )

Proof

Step	Hyp	Ref	Expression
1		sltmul12d.1	$$⊢\phi \to A\in \mathrm{No}$$
2		sltmul12d.2	$$⊢\phi \to B\in \mathrm{No}$$
3		sltmul12d.3	$$⊢\phi \to C\in \mathrm{No}$$
4		sltmul12d.4	Could not format ( ph -> 0s 0s
5		sltmul2	Could not format ( ( ( C e. No /\ 0s ( A ( C x.s A ) ( A ( C x.s A )
6	3 4 1 2 5	syl211anc	Could not format ( ph -> ( A ( C x.s A ) ( A ( C x.s A )