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Axiom ax-addf 10296
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 10299 should be used. Note that uses of ax-addf 10296 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 10247. (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 10215 . . 3 class
21, 1cxp 5309 . 2 class (ℂ × ℂ)
3 caddc 10220 . 2 class +
42, 1, 3wf 6093 1 wff + :(ℂ × ℂ)⟶ℂ
Colors of variables: wff setvar class
This axiom is referenced by:  addex  12040  rlimadd  14592  cnfldplusf  19977  addcn  22878  itg1addlem4  23679  cnaddabloOLD  27763  cnidOLD  27764  cncvcOLD  27765  cnnv  27859  cnnvba  27861  cncph  28001  raddcn  30299  addcomgi  39155
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