Theorem ge0p1rpd

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

	Ref	Expression
Hypotheses	rpgecld.1	$$⊢\phi \to A\in ℝ$$
	ge0p1rp.2	$$⊢\phi \to 0\le A$$
Assertion	ge0p1rpd	$$⊢\phi \to A+1\in {ℝ}^{+}$$

Proof

Step	Hyp	Ref	Expression
1		rpgecld.1	$$⊢\phi \to A\in ℝ$$
2		ge0p1rp.2	$$⊢\phi \to 0\le A$$
3		ge0p1rp	$$⊢\left(A\in ℝ\wedge 0\le A\right)\to A+1\in {ℝ}^{+}$$
4	1 2 3	syl2anc	$$⊢\phi \to A+1\in {ℝ}^{+}$$