ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ax-mulcom Unicode version

Axiom ax-mulcom 7042
Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by theorem axmulcom 7002. Proofs should normally use mulcom 7067 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 6944 . . . 4  class  CC
31, 2wcel 1409 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1409 . . 3  wff  B  e.  CC
63, 5wa 101 . 2  wff  ( A  e.  CC  /\  B  e.  CC )
7 cmul 6951 . . . 4  class  x.
81, 4, 7co 5539 . . 3  class  ( A  x.  B )
94, 1, 7co 5539 . . 3  class  ( B  x.  A )
108, 9wceq 1259 . 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  7067
  Copyright terms: Public domain W3C validator