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Axiom ax-mulass 7044
Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axmulass 7004. Proofs should normally use mulass 7069 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 6944 . . . 4  class  CC
31, 2wcel 1409 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1409 . . 3  wff  B  e.  CC
6 cC . . . 4  class  C
76, 2wcel 1409 . . 3  wff  C  e.  CC
83, 5, 7w3a 896 . 2  wff  ( A  e.  CC  /\  B  e.  CC  /\  C  e.  CC )
9 cmul 6951 . . . . 5  class  x.
101, 4, 9co 5539 . . . 4  class  ( A  x.  B )
1110, 6, 9co 5539 . . 3  class  ( ( A  x.  B )  x.  C )
124, 6, 9co 5539 . . . 4  class  ( B  x.  C )
131, 12, 9co 5539 . . 3  class  ( A  x.  ( B  x.  C ) )
1411, 13wceq 1259 . 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  7069
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