Theorem ltadd1i

Description: Addition to both sides of 'less than'. Theorem I.18 of Apostol p. 20. (Contributed by NM, 21-Jan-1997)

	Ref	Expression
Hypotheses	lt2.1	|- A e. RR
	lt2.2	|- B e. RR
	lt2.3	|- C e. RR
Assertion	ltadd1i	|- ( A < B <-> ( A + C ) < ( B + C ) )

Proof

Step	Hyp	Ref	Expression
1		lt2.1	|- A e. RR
2		lt2.2	|- B e. RR
3		lt2.3	|- C e. RR
4		ltadd1	|- ( ( A e. RR /\ B e. RR /\ C e. RR ) -> ( A < B <-> ( A + C ) < ( B + C ) ) )
5	1 2 3 4	mp3an	|- ( A < B <-> ( A + C ) < ( B + C ) )