Metamath Proof Explorer

Theorem mulneg12

Description: Swap the negative sign in a product. (Contributed by NM, 30-Jul-2004)

Ref Expression
Assertion mulneg12 
|- ( ( A e. CC /\ B e. CC ) -> ( -u A x. B ) = ( A x. -u B ) )

Proof

Step Hyp Ref Expression
1 mulneg1 
 |-  ( ( A e. CC /\ B e. CC ) -> ( -u A x. B ) = -u ( A x. B ) )
2 mulneg2 
 |-  ( ( A e. CC /\ B e. CC ) -> ( A x. -u B ) = -u ( A x. B ) )
3 1 2 eqtr4d 
 |-  ( ( A e. CC /\ B e. CC ) -> ( -u A x. B ) = ( A x. -u B ) )