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Theorem mulassi 7743
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 7719 . 2  |-  ( ( A  e.  CC  /\  B  e.  CC  /\  C  e.  CC )  ->  (
( A  x.  B
)  x.  C )  =  ( A  x.  ( B  x.  C
) ) )
51, 2, 3, 4mp3an 1300 1  |-  ( ( A  x.  B )  x.  C )  =  ( A  x.  ( B  x.  C )
)
Colors of variables: wff set class
Syntax hints:    = wceq 1316    e. wcel 1465  (class class class)co 5742   CCcc 7586    x. cmul 7593
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 7691
This theorem depends on definitions:  df-bi 116  df-3an 949
This theorem is referenced by:  8th4div3  8907  numma  9193  decbin0  9289  sq4e2t8  10358  3dec  10429  ef01bndlem  11390  3dvdsdec  11489  3dvds2dec  11490  sincos4thpi  12848  sincos6thpi  12850
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