Theorem mul01d

Description: Multiplication by 0 . Theorem I.6 of Apostol p. 18. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypothesis	muld.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
Assertion	mul01d	⊢ ( 𝜑 → ( 𝐴 · 0 ) = 0 )

Proof

Step	Hyp	Ref	Expression
1		muld.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
2		mul01	⊢ ( 𝐴 ∈ ℂ → ( 𝐴 · 0 ) = 0 )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 · 0 ) = 0 )