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Theorem mulassi 9104
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 9083 . 2  |-  ( ( A  e.  CC  /\  B  e.  CC  /\  C  e.  CC )  ->  (
( A  x.  B
)  x.  C )  =  ( A  x.  ( B  x.  C
) ) )
51, 2, 3, 4mp3an 1280 1  |-  ( ( A  x.  B )  x.  C )  =  ( A  x.  ( B  x.  C )
)
Colors of variables: wff set class
Syntax hints:    = wceq 1653    e. wcel 1726  (class class class)co 6084   CCcc 8993    x. cmul 9000
This theorem is referenced by:  8th4div3  10196  numma  10418  decbin0  10490  faclbnd4lem1  11589  ef01bndlem  12790  dec5dvds  13405  karatsuba  13425  2exp6  13427  sincos4thpi  20426  sincos6thpi  20428  ang180lem2  20657  ang180lem3  20658  asin1  20739  efiatan2  20762  2efiatan  20763  log2cnv  20789  log2ublem2  20792  log2ublem3  20793  log2ub  20794  bclbnd  21069  bposlem8  21080  ipasslem10  22345  siilem1  22357  normlem0  22616  normlem9  22625  bcseqi  22627  polid2i  22664  ax5seglem7  25879
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-mulass 9061
This theorem depends on definitions:  df-bi 179  df-an 362  df-3an 939
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