Theorem divne0i

Description: The ratio of nonzero numbers is nonzero. (Contributed by NM, 9-Feb-1995)

	Ref	Expression
Hypotheses	divclz.1	|- A e. CC
	divclz.2	|- B e. CC
	divneq0.3	|- A =/= 0
	divneq0.4	|- B =/= 0
Assertion	divne0i	|- ( A / B ) =/= 0

Proof

Step	Hyp	Ref	Expression
1		divclz.1	|- A e. CC
2		divclz.2	|- B e. CC
3		divneq0.3	|- A =/= 0
4		divneq0.4	|- B =/= 0
5		divne0	|- ( ( ( A e. CC /\ A =/= 0 ) /\ ( B e. CC /\ B =/= 0 ) ) -> ( A / B ) =/= 0 )
6	1 3 2 4 5	mp4an	|- ( A / B ) =/= 0