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Axiom ax-addrcl 8798
Description: Closure law for addition in the real subfield of complex numbers. Axiom 6 of 23 for real and complex numbers, justified by theorem axaddrcl 8774. Proofs should normally use readdcl 8820 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 8736 . . . 4  class  RR
31, 2wcel 1684 . . 3  wff  A  e.  RR
4 cB . . . 4  class  B
54, 2wcel 1684 . . 3  wff  B  e.  RR
63, 5wa 358 . 2  wff  ( A  e.  RR  /\  B  e.  RR )
7 caddc 8740 . . . 4  class  +
81, 4, 7co 5858 . . 3  class  ( A  +  B )
98, 2wcel 1684 . 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  8820
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