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Axiom ax-mulcom 7348
Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by theorem axmulcom 7308. Proofs should normally use mulcom 7373 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 7250 . . . 4  class  CC
31, 2wcel 1434 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1434 . . 3  wff  B  e.  CC
63, 5wa 102 . 2  wff  ( A  e.  CC  /\  B  e.  CC )
7 cmul 7257 . . . 4  class  x.
81, 4, 7co 5590 . . 3  class  ( A  x.  B )
94, 1, 7co 5590 . . 3  class  ( B  x.  A )
108, 9wceq 1285 . 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  7373
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