Theorem ltaddposi

Description: Adding a positive number to another number increases it. (Contributed by NM, 25-Aug-1999)

	Ref	Expression
Hypotheses	lt2.1	$$⊢A\in ℝ$$
	lt2.2	$$⊢B\in ℝ$$
Assertion	ltaddposi	$$⊢0<A\leftrightarrow B<B+A$$

Proof

Step	Hyp	Ref	Expression
1		lt2.1	$$⊢A\in ℝ$$
2		lt2.2	$$⊢B\in ℝ$$
3		ltaddpos	$$⊢\left(A\in ℝ\wedge B\in ℝ\right)\to \left(0<A\leftrightarrow B<B+A\right)$$
4	1 2 3	mp2an	$$⊢0<A\leftrightarrow B<B+A$$