Theorem slenegd

Description: Negative of both sides of surreal less-than or equal. (Contributed by Scott Fenton, 14-Mar-2025)

	Ref	Expression
Hypotheses	sltnegd.1	$$⊢\phi \to A\in \mathrm{No}$$
	sltnegd.2	$$⊢\phi \to B\in \mathrm{No}$$
Assertion	slenegd	Could not format assertion : No typesetting found for |- ( ph -> ( A <_s B <-> ( -us ` B ) <_s ( -us ` A ) ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		sltnegd.1	$$⊢\phi \to A\in \mathrm{No}$$
2		sltnegd.2	$$⊢\phi \to B\in \mathrm{No}$$
3		sleneg	Could not format ( ( A e. No /\ B e. No ) -> ( A <_s B <-> ( -us ` B ) <_s ( -us ` A ) ) ) : No typesetting found for |- ( ( A e. No /\ B e. No ) -> ( A <_s B <-> ( -us ` B ) <_s ( -us ` A ) ) ) with typecode |-
4	1 2 3	syl2anc	Could not format ( ph -> ( A <_s B <-> ( -us ` B ) <_s ( -us ` A ) ) ) : No typesetting found for |- ( ph -> ( A <_s B <-> ( -us ` B ) <_s ( -us ` A ) ) ) with typecode |-