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Theorem ablcmnd 39468
 Description: An Abelian group is a commutative monoid. (Contributed by SN, 1-Jun-2024.)
Hypothesis
Ref Expression
ablcmnd.1 (𝜑𝐺 ∈ Abel)
Assertion
Ref Expression
ablcmnd (𝜑𝐺 ∈ CMnd)

Proof of Theorem ablcmnd
StepHypRef Expression
1 ablcmnd.1 . 2 (𝜑𝐺 ∈ Abel)
2 ablcmn 18909 . 2 (𝐺 ∈ Abel → 𝐺 ∈ CMnd)
31, 2syl 17 1 (𝜑𝐺 ∈ CMnd)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 2111  CMndccmn 18902  Abelcabl 18903 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-in 3888  df-abl 18905 This theorem is referenced by:  ringcmnd  39471
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