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Axiom ax-mulcom 8801
Description: Multiplication of complex numbers is commutative. Axiom 8 of 22 for real and complex numbers, justified by theorem axmulcom 8777. Proofs should normally use mulcom 8823 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-mulcom  |-  ( ( A  e.  CC  /\  B  e.  CC )  ->  ( A  x.  B
)  =  ( B  x.  A ) )

Detailed syntax breakdown of Axiom ax-mulcom
StepHypRef Expression
1 cA . . . 4  class  A
2 cc 8735 . . . 4  class  CC
31, 2wcel 1684 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1684 . . 3  wff  B  e.  CC
63, 5wa 358 . 2  wff  ( A  e.  CC  /\  B  e.  CC )
7 cmul 8742 . . . 4  class  x.
81, 4, 7co 5858 . . 3  class  ( A  x.  B )
94, 1, 7co 5858 . . 3  class  ( B  x.  A )
108, 9wceq 1623 . 2  wff  ( A  x.  B )  =  ( B  x.  A
)
116, 10wi 4 1  wff  ( ( A  e.  CC  /\  B  e.  CC )  ->  ( A  x.  B
)  =  ( B  x.  A ) )
Colors of variables: wff set class
This axiom is referenced by:  mulcom  8823
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