Metamath Proof Explorer

Theorem recid

Description: Multiplication of a number and its reciprocal. (Contributed by NM, 25-Oct-1999) (Proof shortened by Mario Carneiro, 27-May-2016)

Ref Expression
Assertion recid 
|- ( ( A e. CC /\ A =/= 0 ) -> ( A x. ( 1 / A ) ) = 1 )

Proof

Step Hyp Ref Expression
1 ax-1cn 
 |-  1 e. CC
2 divcan2 
 |-  ( ( 1 e. CC /\ A e. CC /\ A =/= 0 ) -> ( A x. ( 1 / A ) ) = 1 )
3 1 2 mp3an1 
 |-  ( ( A e. CC /\ A =/= 0 ) -> ( A x. ( 1 / A ) ) = 1 )