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Axiom ax-mulcom 7393
Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by theorem axmulcom 7353. Proofs should normally use mulcom 7418 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 7295 . . . 4 class
31, 2wcel 1436 . . 3 wff 𝐴 ∈ ℂ
4 cB . . . 4 class 𝐵
54, 2wcel 1436 . . 3 wff 𝐵 ∈ ℂ
63, 5wa 102 . 2 wff (𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ)
7 cmul 7302 . . . 4 class ·
81, 4, 7co 5615 . . 3 class (𝐴 · 𝐵)
94, 1, 7co 5615 . . 3 class (𝐵 · 𝐴)
108, 9wceq 1287 . 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  7418
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