Theorem mulassi 7799

Description: Associative law for multiplication. (Contributed by NM, 23-Nov-1994.)

Hypotheses

Ref	Expression
axi.1	|- A e. CC
axi.2	|- B e. CC
axi.3	|- C e. CC

Assertion

Ref	Expression
mulassi	|- ( ( A x. B ) x. C ) = ( A x. ( B x. C ) )

Proof of Theorem mulassi

Step	Hyp	Ref	Expression
1		axi.1	. 2 |- A e. CC
2		axi.2	. 2 |- B e. CC
3		axi.3	. 2 |- C e. CC
4		mulass 7775	. 2 |- ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( ( A x. B ) x. C ) = ( A x. ( B x. C ) ) )
5	1, 2, 3, 4	mp3an 1316	1 |- ( ( A x. B ) x. C ) = ( A x. ( B x. C ) )

Syntax hints:   = wceq 1332   e. wcel 1481  (class class class)co 5782   CCcc 7642   x. cmul 7649

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-mulass 7747

This theorem depends on definitions:  df-bi 116  df-3an 965

This theorem is referenced by:  8th4div3  8963  numma  9249  decbin0  9345  sq4e2t8  10421  3dec  10492  ef01bndlem  11499  3dvdsdec  11598  3dvds2dec  11599  sincos4thpi  12969  sincos6thpi  12971