Theorem ltsubrpd

Description: Subtracting a positive real from another number decreases it. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypotheses	rpgecld.1	|- ( ph -> A e. RR )
	rpgecld.2	|- ( ph -> B e. RR+ )
Assertion	ltsubrpd	|- ( ph -> ( A - B ) < A )

Proof

Step	Hyp	Ref	Expression
1		rpgecld.1	|- ( ph -> A e. RR )
2		rpgecld.2	|- ( ph -> B e. RR+ )
3		ltsubrp	|- ( ( A e. RR /\ B e. RR+ ) -> ( A - B ) < A )
4	1 2 3	syl2anc	|- ( ph -> ( A - B ) < A )