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Axiom ax-mulcom 7390
Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by theorem axmulcom 7350. Proofs should normally use mulcom 7415 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 7292 . . . 4  class  CC
31, 2wcel 1436 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1436 . . 3  wff  B  e.  CC
63, 5wa 102 . 2  wff  ( A  e.  CC  /\  B  e.  CC )
7 cmul 7299 . . . 4  class  x.
81, 4, 7co 5613 . . 3  class  ( A  x.  B )
94, 1, 7co 5613 . . 3  class  ( B  x.  A )
108, 9wceq 1287 . 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  7415
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