Theorem sltnegim

Description: The forward direction of the ordering properties of negation. (Contributed by Scott Fenton, 3-Feb-2025)

	Ref	Expression
Assertion	sltnegim	|- ( ( A e. No /\ B e. No ) -> ( A ( -us ` B )

Proof

Step	Hyp	Ref	Expression
1		negsprop	|- ( ( A e. No /\ B e. No ) -> ( ( -us ` A ) e. No /\ ( A ( -us ` B )
2	1	simprd	|- ( ( A e. No /\ B e. No ) -> ( A ( -us ` B )