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Axiom ax-addf 9100
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 http://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 9103 should be used. Note that uses of ax-addf 9100 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 9051. (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 9019 . . 3  class  CC
21, 1cxp 4905 . 2  class  ( CC 
X.  CC )
3 caddc 9024 . 2  class  +
42, 1, 3wf 5479 1  wff  +  :
( CC  X.  CC )
--> CC
Colors of variables: wff set class
This axiom is referenced by:  addex  10641  rlimadd  12467  cnfldplusf  16759  addcn  18926  itg1addlem4  19620  cnaddablo  21969  cnid  21970  addinv  21971  readdsubgo  21972  zaddsubgo  21973  efghgrp  21992  cnrngo  22022  cncvc  22093  cnnv  22199  cnnvba  22201  cncph  22351  raddcn  24346  addcomgi  27675
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