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Axiom ax-addf 10207
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 10210 should be used. Note that uses of ax-addf 10207 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 10158. (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
StepHypRef Expression
1 cc 10126 . . 3 class
21, 1cxp 5264 . 2 class (ℂ × ℂ)
3 caddc 10131 . 2 class +
42, 1, 3wf 6045 1 wff + :(ℂ × ℂ)⟶ℂ
Colors of variables: wff setvar class
This axiom is referenced by:  addex  12023  rlimadd  14572  cnfldplusf  19975  addcn  22869  itg1addlem4  23665  cnaddabloOLD  27745  cnidOLD  27746  cncvcOLD  27747  cnnv  27841  cnnvba  27843  cncph  27983  raddcn  30284  addcomgi  39162
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