| 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 8223
or
eff 11809. 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 8001. Note that uses of ax-mulf 7997 can be eliminated by using
the defined operation (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑥 · 𝑦)) in place of
·, as seen in mpomulf 8011.
This axiom is justified by Theorem axmulf 7931. (New usage is discouraged.)
(Contributed by NM, 19-Oct-2004.) |
