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Axiom ax-mulrcl 7347
Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axmulrcl 7307. Proofs should normally use remulcl 7373 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 7252 . . . 4  class  RR
31, 2wcel 1434 . . 3  wff  A  e.  RR
4 cB . . . 4  class  B
54, 2wcel 1434 . . 3  wff  B  e.  RR
63, 5wa 102 . 2  wff  ( A  e.  RR  /\  B  e.  RR )
7 cmul 7258 . . . 4  class  x.
81, 4, 7co 5591 . . 3  class  ( A  x.  B )
98, 2wcel 1434 . 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  7373
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