Theorem sltaddsub2d

Description: Surreal less-than relationship between subtraction and addition. (Contributed by Scott Fenton, 28-Feb-2025)

	Ref	Expression
Hypotheses	sltsubadd.1	$$⊢\phi \to A\in \mathrm{No}$$
	sltsubadd.2	$$⊢\phi \to B\in \mathrm{No}$$
	sltsubadd.3	$$⊢\phi \to C\in \mathrm{No}$$
Assertion	sltaddsub2d	Could not format assertion : No typesetting found for |- ( ph -> ( ( A +s B ) B

Proof

Step	Hyp	Ref	Expression
1		sltsubadd.1	$$⊢\phi \to A\in \mathrm{No}$$
2		sltsubadd.2	$$⊢\phi \to B\in \mathrm{No}$$
3		sltsubadd.3	$$⊢\phi \to C\in \mathrm{No}$$
4	1 2	addscomd	Could not format ( ph -> ( A +s B ) = ( B +s A ) ) : No typesetting found for |- ( ph -> ( A +s B ) = ( B +s A ) ) with typecode |-
5	4	breq1d	Could not format ( ph -> ( ( A +s B ) ( B +s A ) ( ( A +s B ) ( B +s A )
6	2 1 3	sltaddsubd	Could not format ( ph -> ( ( B +s A ) B ( ( B +s A ) B
7	5 6	bitrd	Could not format ( ph -> ( ( A +s B ) B ( ( A +s B ) B