Theorem recrecd

Description: A number is equal to the reciprocal of its reciprocal. (Contributed by Mario Carneiro, 27-May-2016)

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

Proof

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