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