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

Axiom ax-addrcl 7205
Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axaddrcl 7165. Proofs should normally use readdcl 7231 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 7112 . . . 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 caddc 7116 . . . 4  class  +
81, 4, 7co 5564 . . 3  class  ( A  +  B )
98, 2wcel 1434 . 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  7231
  Copyright terms: Public domain W3C validator