Theorem mullidd

Description: Identity law for multiplication. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypothesis	addcld.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
Assertion	mullidd	⊢ ( 𝜑 → ( 1 · 𝐴 ) = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		addcld.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
2		mullid	⊢ ( 𝐴 ∈ ℂ → ( 1 · 𝐴 ) = 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → ( 1 · 𝐴 ) = 𝐴 )