Theorem bj-ablssgrpel 37637

Description: Abelian groups are groups (elemental version). This is a shorter proof of ablgrp 19751. (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 37636	. 2 ⊢ Abel ⊆ Grp
2	1	sseli 3911	1 ⊢ (𝐴 ∈ Abel → 𝐴 ∈ Grp)

Syntax hints:   → wi 4   ∈ wcel 2119  Grpcgrp 18900  Abelcabl 19747

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711

This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-v 3433  df-in 3890  df-ss 3900  df-abl 19749

This theorem is referenced by: (None)