Axiom ax-addf 10015

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 10018 should be used. Note that uses of ax-addf 10015 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 9966. (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

Step	Hyp	Ref	Expression
1		cc 9934	. . 3 class CC
2	1, 1	cxp 5112	. 2 class ( CC X. CC )
3		caddc 9939	. 2 class +
4	2, 1, 3	wf 5884	1 wff + : ( CC X. CC ) --> CC

This axiom is referenced by:  addex  11830  rlimadd  14373  cnfldplusf  19773  addcn  22668  itg1addlem4  23466  cnaddabloOLD  27436  cnidOLD  27437  cncvcOLD  27438  cnnv  27532  cnnvba  27534  cncph  27674  raddcn  29975  addcomgi  38660