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Axiom ax-addf 8812
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 8815 should be used. Note that uses of ax-addf 8812 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 8763. (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 8731 . . 3  class  CC
21, 1cxp 4687 . 2  class  ( CC 
X.  CC )
3 caddc 8736 . 2  class  +
42, 1, 3wf 5218 1  wff  +  :
( CC  X.  CC )
--> CC
Colors of variables: wff set class
This axiom is referenced by:  addex  10348  rlimadd  12111  cnfldplusf  16396  addcn  18364  itg1addlem4  19049  cnaddablo  21010  cnid  21011  addinv  21012  readdsubgo  21013  zaddsubgo  21014  efghgrp  21033  cnrngo  21063  cncvc  21132  cnnv  21238  cnnvba  21240  cncph  21390  zintdom  24838  addcomgi  27061
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