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Axiom ax-addf 7749
Description: Addition is an operation on the complex numbers. This deprecated axiom is provided for historical compatibility but is not a bona fide axiom for complex numbers (independent of set theory) since it cannot be interpreted as a first- or second-order statement (see https://us.metamath.org/downloads/schmidt-cnaxioms.pdf). It may be deleted in the future and should be avoided for new theorems. Instead, the less specific addcl 7752 should be used. Note that uses of ax-addf 7749 can be eliminated by using the defined operation  ( x  e.  CC ,  y  e.  CC  |->  ( x  +  y ) ) in place of  +, from which this axiom (with the defined operation in place of  +) follows as a theorem.

This axiom is justified by theorem axaddf 7683. (New usage is discouraged.) (Contributed by NM, 19-Oct-2004.)

Assertion
Ref Expression
ax-addf  |-  +  :
( CC  X.  CC )
--> CC

Detailed syntax breakdown of Axiom ax-addf
StepHypRef Expression
1 cc 7625 . . 3  class  CC
21, 1cxp 4537 . 2  class  ( CC 
X.  CC )
3 caddc 7630 . 2  class  +
42, 1, 3wf 5119 1  wff  +  :
( CC  X.  CC )
--> CC
Colors of variables: wff set class
This axiom is referenced by:  addcncntop  12730
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