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	mul0or.1	|- A e. CC
Assertion	msq0i	|- ( ( A x. A ) = 0 <-> A = 0 )

Proof

Step	Hyp	Ref	Expression
1		mul0or.1	|- A e. CC
2		mul0or	|- ( ( A e. CC /\ A e. CC ) -> ( ( A x. A ) = 0 <-> ( A = 0 \/ A = 0 ) ) )
3	1 1 2	mp2an	|- ( ( A x. A ) = 0 <-> ( A = 0 \/ A = 0 ) )
4		oridm	|- ( ( A = 0 \/ A = 0 ) <-> A = 0 )
5	3 4	bitri	|- ( ( A x. A ) = 0 <-> A = 0 )