Theorem adddi 7105

Description: Alias for ax-distr 7080, for naming consistency with adddii 7129. (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 7080	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 919   = wceq 1284   e. wcel 1433  (class class class)co 5532   CCcc 6979   + caddc 6984   x. cmul 6986

This theorem was proved from axioms:  ax-distr 7080

This theorem is referenced by:  adddir  7110  adddii  7129  adddid  7143  muladd11  7241  cnegex  7286  muladd  7488  nnmulcl  8060  expmul  9521  bernneq  9593  sqoddm1div8  9625  iisermulc2  10178  odd2np1  10272  opoe  10295  opeo  10297  gcdmultiple  10409