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Axiom ax-addcl 7204
Description: Closure law for addition of complex numbers. Axiom for real and complex numbers, justified by theorem axaddcl 7164. Proofs should normally use addcl 7230 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 7111 . . . 4  class  CC
31, 2wcel 1434 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1434 . . 3  wff  B  e.  CC
63, 5wa 102 . 2  wff  ( A  e.  CC  /\  B  e.  CC )
7 caddc 7116 . . . 4  class  +
81, 4, 7co 5564 . . 3  class  ( A  +  B )
98, 2wcel 1434 . 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  7230
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