Axiom ax-addf 11153

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-order 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 11156 should be used. Note that uses of ax-addf 11153 can be eliminated by using the defined operation (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (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 11104. (New usage is discouraged.) (Contributed by NM, 19-Oct-2004.)

Assertion

Ref	Expression
ax-addf	⊢ + :(ℂ × ℂ)⟶ℂ

Detailed syntax breakdown of Axiom ax-addf

Step	Hyp	Ref	Expression
1		cc 11072	. . 3 class ℂ
2	1, 1	cxp 5638	. 2 class (ℂ × ℂ)
3		caddc 11077	. 2 class +
4	2, 1, 3	wf 6509	1 wff + :(ℂ × ℂ)⟶ℂ

This axiom is referenced by:  addex  12954  cnfldadd  21276  dfcnfldOLD  21286  cnfldplusf  21314  addcn  24760  itg1addlem4  25606  cnaddabloOLD  30516  cnidOLD  30517  cncvcOLD  30518  cnnv  30612  cnnvba  30614  cncph  30754  raddcn  33925  addcomgi  44438