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