Metamath Proof Explorer
Description: 0 is a left identity for extended real addition. (Contributed by Glauco Siliprandi, 17-Aug-2020)
|
|
Ref |
Expression |
|
Hypothesis |
xaddid2d.1 |
⊢ ( 𝜑 → 𝐴 ∈ ℝ* ) |
|
Assertion |
xaddid2d |
⊢ ( 𝜑 → ( 0 +𝑒 𝐴 ) = 𝐴 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
xaddid2d.1 |
⊢ ( 𝜑 → 𝐴 ∈ ℝ* ) |
2 |
|
xaddid2 |
⊢ ( 𝐴 ∈ ℝ* → ( 0 +𝑒 𝐴 ) = 𝐴 ) |
3 |
1 2
|
syl |
⊢ ( 𝜑 → ( 0 +𝑒 𝐴 ) = 𝐴 ) |