Theorem leeq2d

Description: Specialization of breq2d to reals and less than. (Contributed by Stanislas Polu, 9-Mar-2020)

	Ref	Expression
Hypotheses	leeq2d.1	|- ( ph -> A <_ C )
	leeq2d.2	|- ( ph -> C = D )
	leeq2d.3	|- ( ph -> A e. RR )
	leeq2d.4	|- ( ph -> C e. RR )
Assertion	leeq2d	|- ( ph -> A <_ D )

Proof

Step	Hyp	Ref	Expression
1		leeq2d.1	|- ( ph -> A <_ C )
2		leeq2d.2	|- ( ph -> C = D )
3		leeq2d.3	|- ( ph -> A e. RR )
4		leeq2d.4	|- ( ph -> C e. RR )
5	1 2	breqtrd	|- ( ph -> A <_ D )