Theorem recne0d

Description: The reciprocal of a nonzero number is nonzero. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypotheses	div1d.1	|- ( ph -> A e. CC )
	reccld.2	|- ( ph -> A =/= 0 )
Assertion	recne0d	|- ( ph -> ( 1 / A ) =/= 0 )

Proof

Step	Hyp	Ref	Expression
1		div1d.1	|- ( ph -> A e. CC )
2		reccld.2	|- ( ph -> A =/= 0 )
3		recne0	|- ( ( A e. CC /\ A =/= 0 ) -> ( 1 / A ) =/= 0 )
4	1 2 3	syl2anc	|- ( ph -> ( 1 / A ) =/= 0 )