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Axiom ax-mulcom 7714
Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by theorem axmulcom 7672. Proofs should normally use mulcom 7742 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 7611 . . . 4 class
31, 2wcel 1480 . . 3 wff 𝐴 ∈ ℂ
4 cB . . . 4 class 𝐵
54, 2wcel 1480 . . 3 wff 𝐵 ∈ ℂ
63, 5wa 103 . 2 wff (𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ)
7 cmul 7618 . . . 4 class ·
81, 4, 7co 5767 . . 3 class (𝐴 · 𝐵)
94, 1, 7co 5767 . . 3 class (𝐵 · 𝐴)
108, 9wceq 1331 . 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  7742
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