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

Axiom ax-addcl 7388
Description: Closure law for addition of complex numbers. Axiom for real and complex numbers, justified by theorem axaddcl 7348. Proofs should normally use addcl 7414 instead, which asserts the same thing but follows our naming conventions for closures. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-addcl  |-  ( ( A  e.  CC  /\  B  e.  CC )  ->  ( A  +  B
)  e.  CC )

Detailed syntax breakdown of Axiom ax-addcl
StepHypRef Expression
1 cA . . . 4  class  A
2 cc 7295 . . . 4  class  CC
31, 2wcel 1436 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1436 . . 3  wff  B  e.  CC
63, 5wa 102 . 2  wff  ( A  e.  CC  /\  B  e.  CC )
7 caddc 7300 . . . 4  class  +
81, 4, 7co 5615 . . 3  class  ( A  +  B )
98, 2wcel 1436 . 2  wff  ( A  +  B )  e.  CC
106, 9wi 4 1  wff  ( ( A  e.  CC  /\  B  e.  CC )  ->  ( A  +  B
)  e.  CC )
Colors of variables: wff set class
This axiom is referenced by:  addcl  7414
  Copyright terms: Public domain W3C validator