Metamath Proof Explorer


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 )