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Axiom ax-addrcl 7389
Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axaddrcl 7349. Proofs should normally use readdcl 7415 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-addrcl  |-  ( ( A  e.  RR  /\  B  e.  RR )  ->  ( A  +  B
)  e.  RR )

Detailed syntax breakdown of Axiom ax-addrcl
StepHypRef Expression
1 cA . . . 4  class  A
2 cr 7296 . . . 4  class  RR
31, 2wcel 1436 . . 3  wff  A  e.  RR
4 cB . . . 4  class  B
54, 2wcel 1436 . . 3  wff  B  e.  RR
63, 5wa 102 . 2  wff  ( A  e.  RR  /\  B  e.  RR )
7 caddc 7300 . . . 4  class  +
81, 4, 7co 5615 . . 3  class  ( A  +  B )
98, 2wcel 1436 . 2  wff  ( A  +  B )  e.  RR
106, 9wi 4 1  wff  ( ( A  e.  RR  /\  B  e.  RR )  ->  ( A  +  B
)  e.  RR )
Colors of variables: wff set class
This axiom is referenced by:  readdcl  7415
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