Theorem ltaddrpd

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

	Ref	Expression
Hypotheses	rpgecld.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
	rpgecld.2	⊢ ( 𝜑 → 𝐵 ∈ ℝ+ )
Assertion	ltaddrpd	⊢ ( 𝜑 → 𝐴 < ( 𝐴 + 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		rpgecld.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		rpgecld.2	⊢ ( 𝜑 → 𝐵 ∈ ℝ+ )
3		ltaddrp	⊢ ( ( 𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ+ ) → 𝐴 < ( 𝐴 + 𝐵 ) )
4	1 2 3	syl2anc	⊢ ( 𝜑 → 𝐴 < ( 𝐴 + 𝐵 ) )