Theorem leadd1i

Description: Addition to both sides of 'less than or equal to'. (Contributed by NM, 11-Aug-1999)

	Ref	Expression
Hypotheses	lt2.1	|- A e. RR
	lt2.2	|- B e. RR
	lt2.3	|- C e. RR
Assertion	leadd1i	|- ( 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		leadd1	|- ( ( 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 ) )