Theorem bj-ablssgrpel 38307

Description: Abelian groups are groups (elemental version). This is a shorter proof of ablgrp 20008. (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 38306	. 2 ⊢ Abel ⊆ Grp
2	1	sseli 3905	1 ⊢ (𝐴 ∈ Abel → 𝐴 ∈ Grp)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2144  Grpcgrp 19153  Abelcabl 20004

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-ss 3897  df-in 4090  df-abl 20006

This theorem is used by: (None)