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Axiom ax-addcl 7870
Description: Closure law for addition of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddcl 7826. Proofs should normally use addcl 7899 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 7772 . . . 4  class  CC
31, 2wcel 2141 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 2141 . . 3  wff  B  e.  CC
63, 5wa 103 . 2  wff  ( A  e.  CC  /\  B  e.  CC )
7 caddc 7777 . . . 4  class  +
81, 4, 7co 5853 . . 3  class  ( A  +  B )
98, 2wcel 2141 . 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  7899
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