Theorem bj-ablssgrpel 33139

Description: Abelian groups are groups (elemental version). This is a shorter proof of ablgrp 18198. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-ablssgrpel	|- ( A e. Abel -> A e. Grp )

Proof of Theorem bj-ablssgrpel

Step	Hyp	Ref	Expression
1		bj-ablssgrp 33138	. 2 |- Abel C_ Grp
2	1	sseli 3599	1 |- ( A e. Abel -> A e. Grp )

Syntax hints:   -> wi 4   e. wcel 1990   Grpcgrp 17422   Abelcabl 18194

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-in 3581  df-ss 3588  df-abl 18196

This theorem is referenced by: (None)