Axiom ax-addf 11186

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 11189 should be used. Note that uses of ax-addf 11186 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 11137. (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 11105	. . 3 class ℂ
2	1, 1	cxp 5674	. 2 class (ℂ × ℂ)
3		caddc 11110	. 2 class +
4	2, 1, 3	wf 6537	1 wff + :(ℂ × ℂ)⟶ℂ

This axiom is referenced by:  addex  12969  rlimaddOLD  15585  cnfldplusf  20965  addcn  24373  itg1addlem4  25208  itg1addlem4OLD  25209  cnaddabloOLD  29822  cnidOLD  29823  cncvcOLD  29824  cnnv  29918  cnnvba  29920  cncph  30060  raddcn  32898  addcomgi  43201