Theorem sltmulneg2d

Description: Multiplication of both sides of surreal less-than by a negative number. (Contributed by Scott Fenton, 14-Mar-2025)

	Ref	Expression
Hypotheses	sltmulneg.1	$$⊢\phi \to A\in \mathrm{No}$$
	sltmulneg.2	$$⊢\phi \to B\in \mathrm{No}$$
	sltmulneg.3	$$⊢\phi \to C\in \mathrm{No}$$
	sltmulneg.4	No typesetting found for |- ( ph -> C
Assertion	sltmulneg2d	Could not format assertion : No typesetting found for |- ( ph -> ( A ( C x.s B )

Proof

Step	Hyp	Ref	Expression
1		sltmulneg.1	$$⊢\phi \to A\in \mathrm{No}$$
2		sltmulneg.2	$$⊢\phi \to B\in \mathrm{No}$$
3		sltmulneg.3	$$⊢\phi \to C\in \mathrm{No}$$
4		sltmulneg.4	Could not format ( ph -> C C
5	1 2 3 4	sltmulneg1d	Could not format ( ph -> ( A ( B x.s C ) ( A ( B x.s C )
6	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 |-
7	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 |-
8	6 7	breq12d	Could not format ( ph -> ( ( B x.s C ) ( C x.s B ) ( ( B x.s C ) ( C x.s B )
9	5 8	bitrd	Could not format ( ph -> ( A ( C x.s B ) ( A ( C x.s B )