Theorem sltnegd

Description: Negative of both sides of surreal less-than. (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	sltnegd	Could not format assertion : No typesetting found for |- ( ph -> ( A ( -us ` B )

Proof

Step	Hyp	Ref	Expression
1		sltnegd.1	$$⊢\phi \to A\in \mathrm{No}$$
2		sltnegd.2	$$⊢\phi \to B\in \mathrm{No}$$
3		sltneg	Could not format ( ( A e. No /\ B e. No ) -> ( A ( -us ` B ) ( A ( -us ` B )
4	1 2 3	syl2anc	Could not format ( ph -> ( A ( -us ` B ) ( A ( -us ` B )