Theorem sltmuldiv2wd

Description: Surreal less-than relationship between division and multiplication. Weak version. (Contributed by Scott Fenton, 14-Mar-2025)

	Ref	Expression
Hypotheses	sltdivmulwd.1	$$⊢\phi \to A\in \mathrm{No}$$
	sltdivmulwd.2	$$⊢\phi \to B\in \mathrm{No}$$
	sltdivmulwd.3	$$⊢\phi \to C\in \mathrm{No}$$
	sltdivmulwd.4	No typesetting found for |- ( ph -> 0s
	sltdivmulwd.5	No typesetting found for |- ( ph -> E. x e. No ( C x.s x ) = 1s ) with typecode |-
Assertion	sltmuldiv2wd	Could not format assertion : No typesetting found for |- ( ph -> ( ( C x.s A ) A

Proof

Step	Hyp	Ref	Expression
1		sltdivmulwd.1	$$⊢\phi \to A\in \mathrm{No}$$
2		sltdivmulwd.2	$$⊢\phi \to B\in \mathrm{No}$$
3		sltdivmulwd.3	$$⊢\phi \to C\in \mathrm{No}$$
4		sltdivmulwd.4	Could not format ( ph -> 0s 0s
5		sltdivmulwd.5	Could not format ( ph -> E. x e. No ( C x.s x ) = 1s ) : No typesetting found for |- ( ph -> E. x e. No ( C x.s x ) = 1s ) with typecode |-
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	6	breq1d	Could not format ( ph -> ( ( A x.s C ) ( C x.s A ) ( ( A x.s C ) ( C x.s A )
8	1 2 3 4 5	sltmuldivwd	Could not format ( ph -> ( ( A x.s C ) A ( ( A x.s C ) A
9	7 8	bitr3d	Could not format ( ph -> ( ( C x.s A ) A ( ( C x.s A ) A