Description: Extended real version of addid2 . (Contributed by Mario Carneiro, 20-Aug-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | xaddid2 | ⊢ ( 𝐴 ∈ ℝ* → ( 0 +𝑒 𝐴 ) = 𝐴 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0xr | ⊢ 0 ∈ ℝ* | |
2 | xaddcom | ⊢ ( ( 0 ∈ ℝ* ∧ 𝐴 ∈ ℝ* ) → ( 0 +𝑒 𝐴 ) = ( 𝐴 +𝑒 0 ) ) | |
3 | 1 2 | mpan | ⊢ ( 𝐴 ∈ ℝ* → ( 0 +𝑒 𝐴 ) = ( 𝐴 +𝑒 0 ) ) |
4 | xaddid1 | ⊢ ( 𝐴 ∈ ℝ* → ( 𝐴 +𝑒 0 ) = 𝐴 ) | |
5 | 3 4 | eqtrd | ⊢ ( 𝐴 ∈ ℝ* → ( 0 +𝑒 𝐴 ) = 𝐴 ) |