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Axiom ax-mulcom 7689
Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by theorem axmulcom 7647. Proofs should normally use mulcom 7717 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 7586 . . . 4  class  CC
31, 2wcel 1465 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1465 . . 3  wff  B  e.  CC
63, 5wa 103 . 2  wff  ( A  e.  CC  /\  B  e.  CC )
7 cmul 7593 . . . 4  class  x.
81, 4, 7co 5742 . . 3  class  ( A  x.  B )
94, 1, 7co 5742 . . 3  class  ( B  x.  A )
108, 9wceq 1316 . 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  7717
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