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Axiom ax-addcl 8797
Description: Closure law for addition of complex numbers. Axiom 4 of 22 for real and complex numbers, justified by theorem axaddcl 8773. Proofs should normally use addcl 8819 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 8735 . . . 4  class  CC
31, 2wcel 1684 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1684 . . 3  wff  B  e.  CC
63, 5wa 358 . 2  wff  ( A  e.  CC  /\  B  e.  CC )
7 caddc 8740 . . . 4  class  +
81, 4, 7co 5858 . . 3  class  ( A  +  B )
98, 2wcel 1684 . 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  8819
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