Theorem recidzi

Description: Multiplication of a number and its reciprocal. (Contributed by NM, 14-May-1999)

	Ref	Expression
Hypothesis	divclz.1	|- A e. CC
Assertion	recidzi	|- ( A =/= 0 -> ( A x. ( 1 / A ) ) = 1 )

Proof

Step	Hyp	Ref	Expression
1		divclz.1	|- A e. CC
2		recid	|- ( ( A e. CC /\ A =/= 0 ) -> ( A x. ( 1 / A ) ) = 1 )
3	1 2	mpan	|- ( A =/= 0 -> ( A x. ( 1 / A ) ) = 1 )