Theorem ge0p1rpd

Description: A nonnegative number plus one is a positive number. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypotheses	rpgecld.1	|- ( ph -> A e. RR )
	ge0p1rp.2	|- ( ph -> 0 <_ A )
Assertion	ge0p1rpd	|- ( ph -> ( A + 1 ) e. RR+ )

Proof

Step	Hyp	Ref	Expression
1		rpgecld.1	|- ( ph -> A e. RR )
2		ge0p1rp.2	|- ( ph -> 0 <_ A )
3		ge0p1rp	|- ( ( A e. RR /\ 0 <_ A ) -> ( A + 1 ) e. RR+ )
4	1 2 3	syl2anc	|- ( ph -> ( A + 1 ) e. RR+ )