ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  mulcomi GIF version

Theorem mulcomi 7061
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 7038 . 2 ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ) → (𝐴 · 𝐵) = (𝐵 · 𝐴))
41, 2, 3mp2an 410 1 (𝐴 · 𝐵) = (𝐵 · 𝐴)
Colors of variables: wff set class
Syntax hints:   = wceq 1257  wcel 1407  (class class class)co 5537  cc 6915   · cmul 6922
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 105  ax-mulcom 7013
This theorem is referenced by:  mulcomli  7062  8th4div3  8171  numma2c  8442  nummul2c  8446  9t11e99  8526  binom2i  9491  fac3  9564
  Copyright terms: Public domain W3C validator