Theorem bj-ablssgrp 37343

Description: Abelian groups are groups. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-ablssgrp	⊢ Abel ⊆ Grp

Proof of Theorem bj-ablssgrp

Step	Hyp	Ref	Expression
1		df-abl 19699	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss1 4186	. 2 ⊢ (Grp ∩ CMnd) ⊆ Grp
3	1, 2	eqsstri 3977	1 ⊢ Abel ⊆ Grp

Syntax hints:   ∩ cin 3897   ⊆ wss 3898  Grpcgrp 18850  CMndccmn 19696  Abelcabl 19697

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2705

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2712  df-cleq 2725  df-clel 2808  df-v 3439  df-in 3905  df-ss 3915  df-abl 19699

This theorem is referenced by:  bj-ablssgrpel  37344