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Axiom ax-mulcl 8795
Description: Closure law for multiplication of complex numbers. Axiom 6 of 22 for real and complex numbers, justified by theorem axmulcl 8771. Proofs should normally use mulcl 8817 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 8731 . . . 4  class  CC
31, 2wcel 1685 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1685 . . 3  wff  B  e.  CC
63, 5wa 360 . 2  wff  ( A  e.  CC  /\  B  e.  CC )
7 cmul 8738 . . . 4  class  x.
81, 4, 7co 5820 . . 3  class  ( A  x.  B )
98, 2wcel 1685 . 2  wff  ( A  x.  B )  e.  CC
106, 9wi 6 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  8817
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