Metamath Proof Explorer


Theorem cjdivi

Description: Complex conjugate distributes over division. (Contributed by NM, 29-Apr-2005) (Revised by Mario Carneiro, 29-May-2016)

Ref Expression
Hypotheses recl.1
|- A e. CC
readdi.2
|- B e. CC
Assertion cjdivi
|- ( B =/= 0 -> ( * ` ( A / B ) ) = ( ( * ` A ) / ( * ` B ) ) )

Proof

Step Hyp Ref Expression
1 recl.1
 |-  A e. CC
2 readdi.2
 |-  B e. CC
3 cjdiv
 |-  ( ( A e. CC /\ B e. CC /\ B =/= 0 ) -> ( * ` ( A / B ) ) = ( ( * ` A ) / ( * ` B ) ) )
4 1 2 3 mp3an12
 |-  ( B =/= 0 -> ( * ` ( A / B ) ) = ( ( * ` A ) / ( * ` B ) ) )