ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ax-addrcl Unicode version

Axiom ax-addrcl 7685
Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axaddrcl 7641. Proofs should normally use readdcl 7714 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 7587 . . . 4  class  RR
31, 2wcel 1465 . . 3  wff  A  e.  RR
4 cB . . . 4  class  B
54, 2wcel 1465 . . 3  wff  B  e.  RR
63, 5wa 103 . 2  wff  ( A  e.  RR  /\  B  e.  RR )
7 caddc 7591 . . . 4  class  +
81, 4, 7co 5742 . . 3  class  ( A  +  B )
98, 2wcel 1465 . 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  7714
  Copyright terms: Public domain W3C validator