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Theorem ablcmnd 39878
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 19071 . 2 (𝐺 ∈ Abel → 𝐺 ∈ CMnd)
31, 2syl 17 1 (𝜑𝐺 ∈ CMnd)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2115  CMndccmn 19064  Abelcabl 19065
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2021  ax-8 2117  ax-9 2125  ax-ext 2712
This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1546  df-ex 1788  df-sb 2076  df-clab 2719  df-cleq 2732  df-clel 2813  df-v 3403  df-in 3864  df-abl 19067
This theorem is referenced by:  ringcmnd  39884
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