Theorem sltmul1d

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	sltmul1d	Could not format assertion : No typesetting found for |- ( ph -> ( A ( A x.s C )

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	1 2 3 4	sltmul2d	Could not format ( ph -> ( A ( C x.s A ) ( A ( C x.s A )
6	1 3	mulscomd	Could not format ( ph -> ( A x.s C ) = ( C x.s A ) ) : No typesetting found for |- ( ph -> ( A x.s C ) = ( C x.s A ) ) with typecode |-
7	2 3	mulscomd	Could not format ( ph -> ( B x.s C ) = ( C x.s B ) ) : No typesetting found for |- ( ph -> ( B x.s C ) = ( C x.s B ) ) with typecode |-
8	6 7	breq12d	Could not format ( ph -> ( ( A x.s C ) ( C x.s A ) ( ( A x.s C ) ( C x.s A )
9	5 8	bitr4d	Could not format ( ph -> ( A ( A x.s C ) ( A ( A x.s C )