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Theorem bj-ablsscmnel 32813
Description: Abelian groups are commutative monoids (elemental version). This is a shorter proof of ablcmn 18139. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-ablsscmnel (𝐴 ∈ Abel → 𝐴 ∈ CMnd)

Proof of Theorem bj-ablsscmnel
StepHypRef Expression
1 bj-ablsscmn 32812 . 2 Abel ⊆ CMnd
21sseli 3584 1 (𝐴 ∈ Abel → 𝐴 ∈ CMnd)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 1987  CMndccmn 18133  Abelcabl 18134
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3192  df-in 3567  df-ss 3574  df-abl 18136
This theorem is referenced by: (None)
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