Metamath Proof Explorer

Theorem mul2negi

Description: Product of two negatives. Theorem I.12 of Apostol p. 18. (Contributed by NM, 14-Feb-1995) (Revised by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses mulm1.1 
|- A e. CC
mulneg.2 
|- B e. CC
Assertion mul2negi 
|- ( -u A x. -u B ) = ( A x. B )

Proof

Step Hyp Ref Expression
1 mulm1.1 
 |-  A e. CC
2 mulneg.2 
 |-  B e. CC
3 mul2neg 
 |-  ( ( A e. CC /\ B e. CC ) -> ( -u A x. -u B ) = ( A x. B ) )
4 1 2 3 mp2an 
 |-  ( -u A x. -u B ) = ( A x. B )