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Theorem mulassi 7093
Description: Associative law for multiplication. (Contributed by NM, 23-Nov-1994.)
Hypotheses
Ref Expression
axi.1 𝐴 ∈ ℂ
axi.2 𝐵 ∈ ℂ
axi.3 𝐶 ∈ ℂ
Assertion
Ref Expression
mulassi ((𝐴 · 𝐵) · 𝐶) = (𝐴 · (𝐵 · 𝐶))

Proof of Theorem mulassi
StepHypRef Expression
1 axi.1 . 2 𝐴 ∈ ℂ
2 axi.2 . 2 𝐵 ∈ ℂ
3 axi.3 . 2 𝐶 ∈ ℂ
4 mulass 7069 . 2 ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ∧ 𝐶 ∈ ℂ) → ((𝐴 · 𝐵) · 𝐶) = (𝐴 · (𝐵 · 𝐶)))
51, 2, 3, 4mp3an 1243 1 ((𝐴 · 𝐵) · 𝐶) = (𝐴 · (𝐵 · 𝐶))
Colors of variables: wff set class
Syntax hints:   = wceq 1259  wcel 1409  (class class class)co 5539  cc 6944   · cmul 6951
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-mulass 7044
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  8th4div3  8200  numma  8469  decbin0  8565  3dec  9579  3dvdsdec  10168  3dvds2dec  10169
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