Theorem addlidd

Description: 0 is a left identity for addition. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypothesis	muld.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
Assertion	addlidd	⊢ ( 𝜑 → ( 0 + 𝐴 ) = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		muld.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
2		addlid	⊢ ( 𝐴 ∈ ℂ → ( 0 + 𝐴 ) = 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → ( 0 + 𝐴 ) = 𝐴 )