Theorem ltaddrp2d

Description: Adding a positive number to another number increases it. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypotheses	rpgecld.1	|- ( ph -> A e. RR )
	rpgecld.2	|- ( ph -> B e. RR+ )
Assertion	ltaddrp2d	|- ( ph -> A < ( B + A ) )

Proof

Step	Hyp	Ref	Expression
1		rpgecld.1	|- ( ph -> A e. RR )
2		rpgecld.2	|- ( ph -> B e. RR+ )
3	1 2	ltaddrpd	|- ( ph -> A < ( A + B ) )
4	1	recnd	|- ( ph -> A e. CC )
5	2	rpcnd	|- ( ph -> B e. CC )
6	4 5	addcomd	|- ( ph -> ( A + B ) = ( B + A ) )
7	3 6	breqtrd	|- ( ph -> A < ( B + A ) )