Theorem ltaddrpd

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

	Ref	Expression
Hypotheses	rpgecld.1	$$⊢\phi \to A\in ℝ$$
	rpgecld.2	$$⊢\phi \to B\in {ℝ}^{+}$$
Assertion	ltaddrpd	$$⊢\phi \to A<A+B$$

Proof

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