Theorem mul01i

Description: Multiplication by 0 . Theorem I.6 of Apostol p. 18. (Contributed by NM, 23-Nov-1994) (Revised by Scott Fenton, 3-Jan-2013)

	Ref	Expression
Hypothesis	mul.1	⊢ 𝐴 ∈ ℂ
Assertion	mul01i	⊢ ( 𝐴 · 0 ) = 0

Proof

Step	Hyp	Ref	Expression
1		mul.1	⊢ 𝐴 ∈ ℂ
2		mul01	⊢ ( 𝐴 ∈ ℂ → ( 𝐴 · 0 ) = 0 )
3	1 2	ax-mp	⊢ ( 𝐴 · 0 ) = 0