Theorem mul01

Description: Multiplication by 0 . Theorem I.6 of Apostol p. 18. (Contributed by NM, 15-May-1999) (Revised by Scott Fenton, 3-Jan-2013)

	Ref	Expression
Assertion	mul01	$$⊢A\in ℂ\to A\cdot 0=0$$

Proof

Step	Hyp	Ref	Expression
1		0cn	$$⊢0\in ℂ$$
2		mulcom	$$⊢\left(A\in ℂ\wedge 0\in ℂ\right)\to A\cdot 0=0\cdot A$$
3	1 2	mpan2	$$⊢A\in ℂ\to A\cdot 0=0\cdot A$$
4		mul02	$$⊢A\in ℂ\to 0\cdot A=0$$
5	3 4	eqtrd	$$⊢A\in ℂ\to A\cdot 0=0$$