Metamath Proof Explorer


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