Theorem subsubs2d

Description: Law for double surreal subtraction. (Contributed by Scott Fenton, 16-Apr-2025)

	Ref	Expression
Hypotheses	subsubs4d.1	$$⊢\phi \to A\in \mathrm{No}$$
	subsubs4d.2	$$⊢\phi \to B\in \mathrm{No}$$
	subsubs4d.3	$$⊢\phi \to C\in \mathrm{No}$$
Assertion	subsubs2d	Could not format assertion : No typesetting found for |- ( ph -> ( A -s ( B -s C ) ) = ( A +s ( C -s B ) ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		subsubs4d.1	$$⊢\phi \to A\in \mathrm{No}$$
2		subsubs4d.2	$$⊢\phi \to B\in \mathrm{No}$$
3		subsubs4d.3	$$⊢\phi \to C\in \mathrm{No}$$
4	2 3	subscld	Could not format ( ph -> ( B -s C ) e. No ) : No typesetting found for |- ( ph -> ( B -s C ) e. No ) with typecode |-
5	1 4	subsvald	Could not format ( ph -> ( A -s ( B -s C ) ) = ( A +s ( -us ` ( B -s C ) ) ) ) : No typesetting found for |- ( ph -> ( A -s ( B -s C ) ) = ( A +s ( -us ` ( B -s C ) ) ) ) with typecode |-
6	2 3	negsubsdi2d	Could not format ( ph -> ( -us ` ( B -s C ) ) = ( C -s B ) ) : No typesetting found for |- ( ph -> ( -us ` ( B -s C ) ) = ( C -s B ) ) with typecode |-
7	6	oveq2d	Could not format ( ph -> ( A +s ( -us ` ( B -s C ) ) ) = ( A +s ( C -s B ) ) ) : No typesetting found for |- ( ph -> ( A +s ( -us ` ( B -s C ) ) ) = ( A +s ( C -s B ) ) ) with typecode |-
8	5 7	eqtrd	Could not format ( ph -> ( A -s ( B -s C ) ) = ( A +s ( C -s B ) ) ) : No typesetting found for |- ( ph -> ( A -s ( B -s C ) ) = ( A +s ( C -s B ) ) ) with typecode |-