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Theorem mulassi 7094
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
StepHypRef Expression
1 axi.1 . 2  |-  A  e.  CC
2 axi.2 . 2  |-  B  e.  CC
3 axi.3 . 2  |-  C  e.  CC
4 mulass 7070 . 2  |-  ( ( A  e.  CC  /\  B  e.  CC  /\  C  e.  CC )  ->  (
( A  x.  B
)  x.  C )  =  ( A  x.  ( B  x.  C
) ) )
51, 2, 3, 4mp3an 1243 1  |-  ( ( A  x.  B )  x.  C )  =  ( A  x.  ( B  x.  C )
)
Colors of variables: wff set class
Syntax hints:    = wceq 1259    e. wcel 1409  (class class class)co 5540   CCcc 6945    x. cmul 6952
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-mulass 7045
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  8th4div3  8201  numma  8470  decbin0  8566  3dec  9586  3dvdsdec  10176  3dvds2dec  10177
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