Theorem sltsubsub3bd

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	sltsubsub3bd	Could not format assertion : No typesetting found for |- ( ph -> ( ( A -s C ) ( 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	1 2 3 4	sltsubsubbd	Could not format ( ph -> ( ( A -s C ) ( A -s B ) ( ( A -s C ) ( A -s B )
6	1 2 3 4	sltsubsub2bd	Could not format ( ph -> ( ( A -s B ) ( D -s C ) ( ( A -s B ) ( D -s C )
7	5 6	bitrd	Could not format ( ph -> ( ( A -s C ) ( D -s C ) ( ( A -s C ) ( D -s C )