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Axiom ax-addf 9867
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 9870 should be used. Note that uses of ax-addf 9867 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 9818. (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 9786 . . 3 class
21, 1cxp 5022 . 2 class (ℂ × ℂ)
3 caddc 9791 . 2 class +
42, 1, 3wf 5782 1 wff + :(ℂ × ℂ)⟶ℂ
Colors of variables: wff setvar class
This axiom is referenced by:  addex  11658  rlimadd  14163  cnfldplusf  19534  addcn  22403  itg1addlem4  23185  cnaddabloOLD  26600  cnidOLD  26601  cncvcOLD  26602  cnnv  26708  cnnvba  26710  cncph  26860  raddcn  29105  addcomgi  37480
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