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Theorem mulcomi 7779
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 7756 . 2 ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ) → (𝐴 · 𝐵) = (𝐵 · 𝐴))
41, 2, 3mp2an 422 1 (𝐴 · 𝐵) = (𝐵 · 𝐴)
Colors of variables: wff set class
Syntax hints:   = wceq 1331  wcel 1480  (class class class)co 5774  cc 7625   · cmul 7632
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107  ax-mulcom 7728
This theorem is referenced by:  mulcomli  7780  8th4div3  8946  numma2c  9234  nummul2c  9238  9t11e99  9318  binom2i  10408  fac3  10485  tanval2ap  11427  sincosq4sgn  12923
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