Theorem xaddcl

Description: The extended real addition operation is closed in extended reals. (Contributed by Mario Carneiro, 20-Aug-2015)

	Ref	Expression
Assertion	xaddcl	⊢ ( ( 𝐴 ∈ ℝ* ∧ 𝐵 ∈ ℝ* ) → ( 𝐴 +𝑒 𝐵 ) ∈ ℝ* )

Proof

Step	Hyp	Ref	Expression
1		xaddf	⊢ +𝑒 : ( ℝ* × ℝ* ) ⟶ ℝ*
2	1	fovcl	⊢ ( ( 𝐴 ∈ ℝ* ∧ 𝐵 ∈ ℝ* ) → ( 𝐴 +𝑒 𝐵 ) ∈ ℝ* )