Metamath Proof Explorer


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* )