Theorem msq0i

Description: A number is zero iff its square is zero (where square is represented using multiplication). (Contributed by NM, 28-Jul-1999)

	Ref	Expression
Hypothesis	msq0i.1	$$⊢A\in ℂ$$
Assertion	msq0i	$$⊢AA=0\leftrightarrow A=0$$

Proof

Step	Hyp	Ref	Expression
1		msq0i.1	$$⊢A\in ℂ$$
2	1 1	mul0ori	$$⊢AA=0\leftrightarrow \left(A=0\vee A=0\right)$$
3		oridm	$$⊢\left(A=0\vee A=0\right)\leftrightarrow A=0$$
4	2 3	bitri	$$⊢AA=0\leftrightarrow A=0$$