Theorem recidd

Description: Multiplication of a number and its reciprocal. (Contributed by Mario Carneiro, 27-May-2016)

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

Proof

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