Metamath Proof Explorer

Theorem recidi

Description: Multiplication of a number and its reciprocal. (Contributed by NM, 9-Feb-1995)

Ref Expression
Hypotheses divclz.1 
|- A e. CC
reccl.2 
|- A =/= 0
Assertion recidi 
|- ( A x. ( 1 / A ) ) = 1

Proof

Step Hyp Ref Expression
1 divclz.1 
 |-  A e. CC
2 reccl.2 
 |-  A =/= 0
3 1 recidzi 
 |-  ( A =/= 0 -> ( A x. ( 1 / A ) ) = 1 )
4 2 3 ax-mp 
 |-  ( A x. ( 1 / A ) ) = 1