Theorem mulassi 8030

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 8005	. 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 1348	1 |- ( ( A x. B ) x. C ) = ( A x. ( B x. C ) )

Syntax hints:   = wceq 1364   e. wcel 2164  (class class class)co 5919   CCcc 7872   x. cmul 7879

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-mulass 7977

This theorem depends on definitions:  df-bi 117  df-3an 982

This theorem is referenced by:  8th4div3  9204  numma  9494  decbin0  9590  sq4e2t8  10711  3dec  10788  ef01bndlem  11902  3dvdsdec  12009  3dvds2dec  12010  sincos4thpi  15016  sincos6thpi  15018  2lgsoddprmlem3d  15267