Theorem bj-ablssgrpel 37730

Description: Abelian groups are groups (elemental version). This is a shorter proof of ablgrp 19816. (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 37729	. 2 ⊢ Abel ⊆ Grp
2	1	sseli 3930	1 ⊢ (𝐴 ∈ Abel → 𝐴 ∈ Grp)

Syntax hints:   → wi 4   ∈ wcel 2141  Grpcgrp 18966  Abelcabl 19812

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-ext 2733

This theorem depends on definitions:  df-bi 209  df-an 400  df-tru 1562  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-v 3455  df-in 3909  df-ss 3919  df-abl 19814

This theorem is referenced by: (None)