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Theorem bj-ablssgrpel 36809
Description: Abelian groups are groups (elemental version). This is a shorter proof of ablgrp 19739. (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 36808 . 2 Abel ⊆ Grp
21sseli 3969 1 (𝐴 ∈ Abel → 𝐴 ∈ Grp)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098  Grpcgrp 18889  Abelcabl 19735
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-v 3465  df-in 3948  df-ss 3958  df-abl 19737
This theorem is referenced by: (None)
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