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Axiom ax-mulass 7931
Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by Theorem axmulass 7889. Proofs should normally use mulass 7959 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-mulass  |-  ( ( A  e.  CC  /\  B  e.  CC  /\  C  e.  CC )  ->  (
( A  x.  B
)  x.  C )  =  ( A  x.  ( B  x.  C
) ) )

Detailed syntax breakdown of Axiom ax-mulass
StepHypRef Expression
1 cA . . . 4  class  A
2 cc 7826 . . . 4  class  CC
31, 2wcel 2159 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 2159 . . 3  wff  B  e.  CC
6 cC . . . 4  class  C
76, 2wcel 2159 . . 3  wff  C  e.  CC
83, 5, 7w3a 979 . 2  wff  ( A  e.  CC  /\  B  e.  CC  /\  C  e.  CC )
9 cmul 7833 . . . . 5  class  x.
101, 4, 9co 5890 . . . 4  class  ( A  x.  B )
1110, 6, 9co 5890 . . 3  class  ( ( A  x.  B )  x.  C )
124, 6, 9co 5890 . . . 4  class  ( B  x.  C )
131, 12, 9co 5890 . . 3  class  ( A  x.  ( B  x.  C ) )
1411, 13wceq 1363 . 2  wff  ( ( A  x.  B )  x.  C )  =  ( A  x.  ( B  x.  C )
)
158, 14wi 4 1  wff  ( ( A  e.  CC  /\  B  e.  CC  /\  C  e.  CC )  ->  (
( A  x.  B
)  x.  C )  =  ( A  x.  ( B  x.  C
) ) )
Colors of variables: wff set class
This axiom is referenced by:  mulass  7959
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