Metamath Proof Explorer

Theorem adddi

Description: Alias for ax-distr , for naming consistency with adddii . (Contributed by NM, 10-Mar-2008)

Ref Expression
Assertion adddi 
|- ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( A x. ( B + C ) ) = ( ( A x. B ) + ( A x. C ) ) )

Proof

Step Hyp Ref Expression
1 ax-distr 
 |-  ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( A x. ( B + C ) ) = ( ( A x. B ) + ( A x. C ) ) )