Theorem nltled

Description: 'Not less than ' implies 'less than or equal to'. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Hypotheses	ltd.1	|- ( ph -> A e. RR )
	ltd.2	|- ( ph -> B e. RR )
	nltled.1	|- ( ph -> -. B < A )
Assertion	nltled	|- ( ph -> A <_ B )

Proof

Step	Hyp	Ref	Expression
1		ltd.1	|- ( ph -> A e. RR )
2		ltd.2	|- ( ph -> B e. RR )
3		nltled.1	|- ( ph -> -. B < A )
4	1 2	lenltd	|- ( ph -> ( A <_ B <-> -. B < A ) )
5	3 4	mpbird	|- ( ph -> A <_ B )