Theorem bj-ablssgrpel 36751

Description: Abelian groups are groups (elemental version). This is a shorter proof of ablgrp 19734. (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 36750	. 2 ⊢ Abel ⊆ Grp
2	1	sseli 3975	1 ⊢ (𝐴 ∈ Abel → 𝐴 ∈ Grp)

Syntax hints:   → wi 4   ∈ wcel 2099  Grpcgrp 18884  Abelcabl 19730

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-v 3472  df-in 3952  df-ss 3962  df-abl 19732

This theorem is referenced by: (None)