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Theorem mulcomi 7187
Description: Commutative law for multiplication. (Contributed by NM, 23-Nov-1994.)
Hypotheses
Ref Expression
axi.1 𝐴 ∈ ℂ
axi.2 𝐵 ∈ ℂ
Assertion
Ref Expression
mulcomi (𝐴 · 𝐵) = (𝐵 · 𝐴)

Proof of Theorem mulcomi
StepHypRef Expression
1 axi.1 . 2 𝐴 ∈ ℂ
2 axi.2 . 2 𝐵 ∈ ℂ
3 mulcom 7164 . 2 ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ) → (𝐴 · 𝐵) = (𝐵 · 𝐴))
41, 2, 3mp2an 417 1 (𝐴 · 𝐵) = (𝐵 · 𝐴)
Colors of variables: wff set class
Syntax hints:   = wceq 1285  wcel 1434  (class class class)co 5543  cc 7041   · cmul 7048
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 106  ax-mulcom 7139
This theorem is referenced by:  mulcomli  7188  8th4div3  8317  numma2c  8603  nummul2c  8607  9t11e99  8687  binom2i  9680  fac3  9756
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