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Theorem bj-ablssgrpel 32316
 Description: Abelian groups are groups (elemental version). This is a shorter proof of ablgrp 18021. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-ablssgrpel (𝐴 ∈ Abel → 𝐴 ∈ Grp)

Proof of Theorem bj-ablssgrpel
StepHypRef Expression
1 bj-ablssgrp 32315 . 2 Abel ⊆ Grp
21sseli 3564 1 (𝐴 ∈ Abel → 𝐴 ∈ Grp)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 1977  Grpcgrp 17245  Abelcabl 18017 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-in 3547  df-ss 3554  df-abl 18019 This theorem is referenced by: (None)
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