Theorem adddi 7013

Description: Alias for ax-distr 6988, for naming consistency with adddii 7037. (Contributed by NM, 10-Mar-2008.)

Assertion

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

Proof of Theorem adddi

Step	Hyp	Ref	Expression
1		ax-distr 6988	1 |- ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( A x. ( B + C ) ) = ( ( A x. B ) + ( A x. C ) ) )

Syntax hints:   -> wi 4   /\ w3a 885   = wceq 1243   e. wcel 1393  (class class class)co 5512   CCcc 6887   + caddc 6892   x. cmul 6894

This theorem was proved from axioms:  ax-distr 6988

This theorem is referenced by:  adddir  7018  adddii  7037  adddid  7051  muladd11  7146  cnegex  7189  muladd  7381  nnmulcl  7935  expmul  9300  bernneq  9369  iisermulc2  9860