Theorem xaddid2d

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 )