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Axiom ax-mulrcl 7594
Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axmulrcl 7554. Proofs should normally use remulcl 7620 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 7499 . . . 4  class  RR
31, 2wcel 1448 . . 3  wff  A  e.  RR
4 cB . . . 4  class  B
54, 2wcel 1448 . . 3  wff  B  e.  RR
63, 5wa 103 . 2  wff  ( A  e.  RR  /\  B  e.  RR )
7 cmul 7505 . . . 4  class  x.
81, 4, 7co 5706 . . 3  class  ( A  x.  B )
98, 2wcel 1448 . 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  7620
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