Theorem bj-ablssgrpel 37954

Description: Abelian groups are groups (elemental version). This is a shorter proof of ablgrp 19879. (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 37953	. 2 ⊢ Abel ⊆ Grp
2	1	sseli 3934	1 ⊢ (𝐴 ∈ Abel → 𝐴 ∈ Grp)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2146  Grpcgrp 19024  Abelcabl 19875

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459  df-in 3913  df-ss 3923  df-abl 19877

This theorem is used by: (None)