Theorem xaddlidd

Description: 0 is a left identity for extended real addition. (Contributed by Glauco Siliprandi, 17-Aug-2020)

	Ref	Expression
Hypothesis	xaddlidd.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ* )
Assertion	xaddlidd	⊢ ( 𝜑 → ( 0 +𝑒 𝐴 ) = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		xaddlidd.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ* )
2		xaddlid	⊢ ( 𝐴 ∈ ℝ* → ( 0 +𝑒 𝐴 ) = 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → ( 0 +𝑒 𝐴 ) = 𝐴 )