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Axiom ax-mulcom 7507
Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by theorem axmulcom 7467. Proofs should normally use mulcom 7532 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 7409 . . . 4 class
31, 2wcel 1439 . . 3 wff 𝐴 ∈ ℂ
4 cB . . . 4 class 𝐵
54, 2wcel 1439 . . 3 wff 𝐵 ∈ ℂ
63, 5wa 103 . 2 wff (𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ)
7 cmul 7416 . . . 4 class ·
81, 4, 7co 5666 . . 3 class (𝐴 · 𝐵)
94, 1, 7co 5666 . . 3 class (𝐵 · 𝐴)
108, 9wceq 1290 . 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  7532
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