Theorem bj-ablssgrpel 37256

Description: Abelian groups are groups (elemental version). This is a shorter proof of ablgrp 19799. (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 37255	. 2 ⊢ Abel ⊆ Grp
2	1	sseli 3978	1 ⊢ (𝐴 ∈ Abel → 𝐴 ∈ Grp)

Syntax hints:   → wi 4   ∈ wcel 2108  Grpcgrp 18947  Abelcabl 19795

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-in 3957  df-ss 3967  df-abl 19797

This theorem is referenced by: (None)