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Axiom ax-addcl 7684
Description: Closure law for addition of complex numbers. Axiom for real and complex numbers, justified by theorem axaddcl 7640. Proofs should normally use addcl 7713 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 7586 . . . 4  class  CC
31, 2wcel 1465 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1465 . . 3  wff  B  e.  CC
63, 5wa 103 . 2  wff  ( A  e.  CC  /\  B  e.  CC )
7 caddc 7591 . . . 4  class  +
81, 4, 7co 5742 . . 3  class  ( A  +  B )
98, 2wcel 1465 . 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  7713
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