Metamath Proof Explorer

Theorem mulneg2i

Description: Product with negative is negative of product. (Contributed by NM, 31-Jul-1999) (Revised by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses mulm1.1 
|- A e. CC
mulneg.2 
|- B e. CC
Assertion mulneg2i 
|- ( A x. -u B ) = -u ( A x. B )

Proof

Step Hyp Ref Expression
1 mulm1.1 
 |-  A e. CC
2 mulneg.2 
 |-  B e. CC
3 mulneg2 
 |-  ( ( A e. CC /\ B e. CC ) -> ( A x. -u B ) = -u ( A x. B ) )
4 1 2 3 mp2an 
 |-  ( A x. -u B ) = -u ( A x. B )