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Axiom ax-addcl 7037
Description: Closure law for addition of complex numbers. Axiom for real and complex numbers, justified by theorem axaddcl 6997. Proofs should normally use addcl 7063 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 6944 . . . 4  class  CC
31, 2wcel 1409 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1409 . . 3  wff  B  e.  CC
63, 5wa 101 . 2  wff  ( A  e.  CC  /\  B  e.  CC )
7 caddc 6949 . . . 4  class  +
81, 4, 7co 5539 . . 3  class  ( A  +  B )
98, 2wcel 1409 . 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  7063
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