Theorem leeq1d

Description: Specialization of breq1d to reals and less than. (Contributed by Stanislas Polu, 9-Mar-2020)

	Ref	Expression
Hypotheses	leeq1d.1	|- ( ph -> A <_ C )
	leeq1d.2	|- ( ph -> A = B )
	leeq1d.3	|- ( ph -> A e. RR )
	leeq1d.4	|- ( ph -> C e. RR )
Assertion	leeq1d	|- ( ph -> B <_ C )

Proof

Step	Hyp	Ref	Expression
1		leeq1d.1	|- ( ph -> A <_ C )
2		leeq1d.2	|- ( ph -> A = B )
3		leeq1d.3	|- ( ph -> A e. RR )
4		leeq1d.4	|- ( ph -> C e. RR )
5	2 1	eqbrtrrd	|- ( ph -> B <_ C )