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Axiom ax-mulcom 7741
Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by theorem axmulcom 7699. Proofs should normally use mulcom 7769 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 7638 . . . 4  class  CC
31, 2wcel 1481 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1481 . . 3  wff  B  e.  CC
63, 5wa 103 . 2  wff  ( A  e.  CC  /\  B  e.  CC )
7 cmul 7645 . . . 4  class  x.
81, 4, 7co 5778 . . 3  class  ( A  x.  B )
94, 1, 7co 5778 . . 3  class  ( B  x.  A )
108, 9wceq 1332 . 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  7769
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