Theorem bj-ablssgrpel 37317

Description: Abelian groups are groups (elemental version). This is a shorter proof of ablgrp 19698. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-ablssgrpel	⊢ (𝐴 ∈ Abel → 𝐴 ∈ Grp)

Proof of Theorem bj-ablssgrpel

Step	Hyp	Ref	Expression
1		bj-ablssgrp 37316	. 2 ⊢ Abel ⊆ Grp
2	1	sseli 3930	1 ⊢ (𝐴 ∈ Abel → 𝐴 ∈ Grp)

Syntax hints:   → wi 4   ∈ wcel 2111  Grpcgrp 18846  Abelcabl 19694

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-v 3438  df-in 3909  df-ss 3919  df-abl 19696

This theorem is referenced by: (None)