Theorem ltaddsubi

Description: 'Less than' relationship between subtraction and addition. (Contributed by NM, 14-May-1999)

	Ref	Expression
Hypotheses	lt2.1	|- A e. RR
	lt2.2	|- B e. RR
	lt2.3	|- C e. RR
Assertion	ltaddsubi	|- ( ( A + B ) < C <-> A < ( C - B ) )

Proof

Step	Hyp	Ref	Expression
1		lt2.1	|- A e. RR
2		lt2.2	|- B e. RR
3		lt2.3	|- C e. RR
4		ltaddsub	|- ( ( A e. RR /\ B e. RR /\ C e. RR ) -> ( ( A + B ) < C <-> A < ( C - B ) ) )
5	1 2 3 4	mp3an	|- ( ( A + B ) < C <-> A < ( C - B ) )