Theorem mulassi 8181

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 8156	. 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 1371	1 |- ( ( A x. B ) x. C ) = ( A x. ( B x. C ) )

Syntax hints:   = wceq 1395   e. wcel 2200  (class class class)co 6013   CCcc 8023   x. cmul 8030

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 8128

This theorem depends on definitions:  df-bi 117  df-3an 1004

This theorem is referenced by:  8th4div3  9356  numma  9647  decbin0  9743  sq4e2t8  10892  3dec  10969  ef01bndlem  12310  3dvdsdec  12419  3dvds2dec  12420  dec5dvds  12978  karatsuba  12996  sincos4thpi  15557  sincos6thpi  15559  2lgsoddprmlem3d  15832