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Axiom ax-mulrcl 7040
Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axmulrcl 7000. Proofs should normally use remulcl 7066 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 6945 . . . 4  class  RR
31, 2wcel 1409 . . 3  wff  A  e.  RR
4 cB . . . 4  class  B
54, 2wcel 1409 . . 3  wff  B  e.  RR
63, 5wa 101 . 2  wff  ( A  e.  RR  /\  B  e.  RR )
7 cmul 6951 . . . 4  class  x.
81, 4, 7co 5539 . . 3  class  ( A  x.  B )
98, 2wcel 1409 . 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  7066
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