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Axiom ax-mulcom 7596
Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by theorem axmulcom 7556. Proofs should normally use mulcom 7621 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 7498 . . . 4  class  CC
31, 2wcel 1448 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1448 . . 3  wff  B  e.  CC
63, 5wa 103 . 2  wff  ( A  e.  CC  /\  B  e.  CC )
7 cmul 7505 . . . 4  class  x.
81, 4, 7co 5706 . . 3  class  ( A  x.  B )
94, 1, 7co 5706 . . 3  class  ( B  x.  A )
108, 9wceq 1299 . 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  7621
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