Theorem xaddid1d

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

	Ref	Expression
Hypothesis	xaddid1d.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ* )
Assertion	xaddid1d	⊢ ( 𝜑 → ( 𝐴 +𝑒 0 ) = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		xaddid1d.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ* )
2		xaddid1	⊢ ( 𝐴 ∈ ℝ* → ( 𝐴 +𝑒 0 ) = 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 +𝑒 0 ) = 𝐴 )