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Axiom ax-mulcl 7911
Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulcl 7867. Proofs should normally use mulcl 7940 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 7811 . . . 4  class  CC
31, 2wcel 2148 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 2148 . . 3  wff  B  e.  CC
63, 5wa 104 . 2  wff  ( A  e.  CC  /\  B  e.  CC )
7 cmul 7818 . . . 4  class  x.
81, 4, 7co 5877 . . 3  class  ( A  x.  B )
98, 2wcel 2148 . 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  7940
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