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Axiom ax-mulcl 7939
Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulcl 7895. Proofs should normally use mulcl 7968 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-mulcl ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ) → (𝐴 · 𝐵) ∈ ℂ)

Detailed syntax breakdown of Axiom ax-mulcl
StepHypRef Expression
1 cA . . . 4 class 𝐴
2 cc 7839 . . . 4 class
31, 2wcel 2160 . . 3 wff 𝐴 ∈ ℂ
4 cB . . . 4 class 𝐵
54, 2wcel 2160 . . 3 wff 𝐵 ∈ ℂ
63, 5wa 104 . 2 wff (𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ)
7 cmul 7846 . . . 4 class ·
81, 4, 7co 5896 . . 3 class (𝐴 · 𝐵)
98, 2wcel 2160 . 2 wff (𝐴 · 𝐵) ∈ ℂ
106, 9wi 4 1 wff ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ) → (𝐴 · 𝐵) ∈ ℂ)
Colors of variables: wff set class
This axiom is referenced by:  mulcl  7968
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