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	$$⊢\phi \to A\in ℂ$$
Assertion	mul01d	$$⊢\phi \to A\cdot 0=0$$

Proof

Step	Hyp	Ref	Expression
1		muld.1	$$⊢\phi \to A\in ℂ$$
2		mul01	$$⊢A\in ℂ\to A\cdot 0=0$$
3	1 2	syl	$$⊢\phi \to A\cdot 0=0$$