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Axiom ax-mulrcl 8816
Description: Closure law for multiplication in the real subfield of complex numbers. Axiom 7 of 22 for real and complex numbers, justified by theorem axmulrcl 8792. Proofs should normally use remulcl 8838 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 8752 . . . 4  class  RR
31, 2wcel 1696 . . 3  wff  A  e.  RR
4 cB . . . 4  class  B
54, 2wcel 1696 . . 3  wff  B  e.  RR
63, 5wa 358 . 2  wff  ( A  e.  RR  /\  B  e.  RR )
7 cmul 8758 . . . 4  class  x.
81, 4, 7co 5874 . . 3  class  ( A  x.  B )
98, 2wcel 1696 . 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  8838
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