Theorem mulne0i

Description: The product of two nonzero numbers is nonzero. (Contributed by NM, 15-Feb-1995)

	Ref	Expression
Hypotheses	muln0.1	|- A e. CC
	muln0.2	|- B e. CC
	muln0.3	|- A =/= 0
	muln0.4	|- B =/= 0
Assertion	mulne0i	|- ( A x. B ) =/= 0

Proof

Step	Hyp	Ref	Expression
1		muln0.1	|- A e. CC
2		muln0.2	|- B e. CC
3		muln0.3	|- A =/= 0
4		muln0.4	|- B =/= 0
5		mulne0	|- ( ( ( A e. CC /\ A =/= 0 ) /\ ( B e. CC /\ B =/= 0 ) ) -> ( A x. B ) =/= 0 )
6	1 3 2 4 5	mp4an	|- ( A x. B ) =/= 0