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Axiom ax-mulcom 6985
 Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by theorem axmulcom 6945. Proofs should normally use mulcom 7010 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-mulcom ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ) → (𝐴 · 𝐵) = (𝐵 · 𝐴))

Detailed syntax breakdown of Axiom ax-mulcom
StepHypRef Expression
1 cA . . . 4 class 𝐴
2 cc 6887 . . . 4 class
31, 2wcel 1393 . . 3 wff 𝐴 ∈ ℂ
4 cB . . . 4 class 𝐵
54, 2wcel 1393 . . 3 wff 𝐵 ∈ ℂ
63, 5wa 97 . 2 wff (𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ)
7 cmul 6894 . . . 4 class ·
81, 4, 7co 5512 . . 3 class (𝐴 · 𝐵)
94, 1, 7co 5512 . . 3 class (𝐵 · 𝐴)
108, 9wceq 1243 . 2 wff (𝐴 · 𝐵) = (𝐵 · 𝐴)
116, 10wi 4 1 wff ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ) → (𝐴 · 𝐵) = (𝐵 · 𝐴))
 Colors of variables: wff set class This axiom is referenced by:  mulcom  7010
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