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Axiom ax-mulcl 7206
Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by theorem axmulcl 7166. Proofs should normally use mulcl 7232 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 7111 . . . 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 7118 . . . 4  class  x.
81, 4, 7co 5564 . . 3  class  ( A  x.  B )
98, 2wcel 1434 . 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  7232
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