Theorem sltsubsub2bd

Description: Equivalence for the surreal less-than relationship between differences. (Contributed by Scott Fenton, 21-Feb-2025)

	Ref	Expression
Hypotheses	sltsubsubbd.1	$$⊢\phi \to A\in \mathrm{No}$$
	sltsubsubbd.2	$$⊢\phi \to B\in \mathrm{No}$$
	sltsubsubbd.3	$$⊢\phi \to C\in \mathrm{No}$$
	sltsubsubbd.4	$$⊢\phi \to D\in \mathrm{No}$$
Assertion	sltsubsub2bd	Could not format assertion : No typesetting found for |- ( ph -> ( ( A -s B ) ( D -s C )

Proof

Step	Hyp	Ref	Expression
1		sltsubsubbd.1	$$⊢\phi \to A\in \mathrm{No}$$
2		sltsubsubbd.2	$$⊢\phi \to B\in \mathrm{No}$$
3		sltsubsubbd.3	$$⊢\phi \to C\in \mathrm{No}$$
4		sltsubsubbd.4	$$⊢\phi \to D\in \mathrm{No}$$
5	4 3	subscld	Could not format ( ph -> ( D -s C ) e. No ) : No typesetting found for |- ( ph -> ( D -s C ) e. No ) with typecode |-
6	2 1	subscld	Could not format ( ph -> ( B -s A ) e. No ) : No typesetting found for |- ( ph -> ( B -s A ) e. No ) with typecode |-
7	5 6	sltnegd	Could not format ( ph -> ( ( D -s C ) ( -us ` ( B -s A ) ) ( ( D -s C ) ( -us ` ( B -s A ) )
8	2 1	negsubsdi2d	Could not format ( ph -> ( -us ` ( B -s A ) ) = ( A -s B ) ) : No typesetting found for |- ( ph -> ( -us ` ( B -s A ) ) = ( A -s B ) ) with typecode |-
9	4 3	negsubsdi2d	Could not format ( ph -> ( -us ` ( D -s C ) ) = ( C -s D ) ) : No typesetting found for |- ( ph -> ( -us ` ( D -s C ) ) = ( C -s D ) ) with typecode |-
10	8 9	breq12d	Could not format ( ph -> ( ( -us ` ( B -s A ) ) ( A -s B ) ( ( -us ` ( B -s A ) ) ( A -s B )
11	7 10	bitr2d	Could not format ( ph -> ( ( A -s B ) ( D -s C ) ( ( A -s B ) ( D -s C )