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Theorem mulassi 7782
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 7758 . 2  |-  ( ( A  e.  CC  /\  B  e.  CC  /\  C  e.  CC )  ->  (
( A  x.  B
)  x.  C )  =  ( A  x.  ( B  x.  C
) ) )
51, 2, 3, 4mp3an 1315 1  |-  ( ( A  x.  B )  x.  C )  =  ( A  x.  ( B  x.  C )
)
Colors of variables: wff set class
Syntax hints:    = wceq 1331    e. wcel 1480  (class class class)co 5774   CCcc 7625    x. cmul 7632
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 7730
This theorem depends on definitions:  df-bi 116  df-3an 964
This theorem is referenced by:  8th4div3  8946  numma  9232  decbin0  9328  sq4e2t8  10397  3dec  10468  ef01bndlem  11470  3dvdsdec  11569  3dvds2dec  11570  sincos4thpi  12931  sincos6thpi  12933
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