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Axiom ax-mulcl 7039
Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by theorem axmulcl 6999. Proofs should normally use mulcl 7065 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-mulcl  |-  ( ( A  e.  CC  /\  B  e.  CC )  ->  ( A  x.  B
)  e.  CC )

Detailed syntax breakdown of Axiom ax-mulcl
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 )
98, 2wcel 1409 . 2  wff  ( A  x.  B )  e.  CC
106, 9wi 4 1  wff  ( ( A  e.  CC  /\  B  e.  CC )  ->  ( A  x.  B
)  e.  CC )
Colors of variables: wff set class
This axiom is referenced by:  mulcl  7065
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