Theorem int-ineqtransd

Description: InequalityTransitivity generator rule. (Contributed by Stanislas Polu, 7-Apr-2020)

	Ref	Expression
Hypotheses	int-ineqtransd.1	|- ( ph -> A e. RR )
	int-ineqtransd.2	|- ( ph -> B e. RR )
	int-ineqtransd.3	|- ( ph -> C e. RR )
	int-ineqtransd.4	|- ( ph -> B <_ A )
	int-ineqtransd.5	|- ( ph -> C <_ B )
Assertion	int-ineqtransd	|- ( ph -> C <_ A )

Proof

Step	Hyp	Ref	Expression
1		int-ineqtransd.1	|- ( ph -> A e. RR )
2		int-ineqtransd.2	|- ( ph -> B e. RR )
3		int-ineqtransd.3	|- ( ph -> C e. RR )
4		int-ineqtransd.4	|- ( ph -> B <_ A )
5		int-ineqtransd.5	|- ( ph -> C <_ B )
6	3 2 1 5 4	letrd	|- ( ph -> C <_ A )