| Description: Multiplication is an
operation on the complex numbers. This axiom tells
us that · is defined only on complex
numbers which is analogous to
the way that other operations are defined, for example see subf 8364
or
eff 12195. However, while Metamath can handle this
axiom, if we wish to work
with weaker complex number axioms, we can avoid it by using the less
specific mulcl 8142. Note that uses of ax-mulf 8138 can be eliminated by using
the defined operation (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑥 · 𝑦)) in place of
·, as seen in mpomulf 8152.
This axiom is justified by Theorem axmulf 8072. (New usage is discouraged.)
(Contributed by NM, 19-Oct-2004.) |
