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.) |