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Axiom ax-mulrcl 7901
Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulrcl 7857. Proofs should normally use remulcl 7930 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-mulrcl  |-  ( ( A  e.  RR  /\  B  e.  RR )  ->  ( A  x.  B
)  e.  RR )

Detailed syntax breakdown of Axiom ax-mulrcl
StepHypRef Expression
1 cA . . . 4  class  A
2 cr 7801 . . . 4  class  RR
31, 2wcel 2148 . . 3  wff  A  e.  RR
4 cB . . . 4  class  B
54, 2wcel 2148 . . 3  wff  B  e.  RR
63, 5wa 104 . 2  wff  ( A  e.  RR  /\  B  e.  RR )
7 cmul 7807 . . . 4  class  x.
81, 4, 7co 5869 . . 3  class  ( A  x.  B )
98, 2wcel 2148 . 2  wff  ( A  x.  B )  e.  RR
106, 9wi 4 1  wff  ( ( A  e.  RR  /\  B  e.  RR )  ->  ( A  x.  B
)  e.  RR )
Colors of variables: wff set class
This axiom is referenced by:  remulcl  7930
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