Theorem bj-ablssgrp 35057

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 19020	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss1 4117	. 2 ⊢ (Grp ∩ CMnd) ⊆ Grp
3	1, 2	eqsstri 3909	1 ⊢ Abel ⊆ Grp

Syntax hints:   ∩ cin 3840   ⊆ wss 3841  Grpcgrp 18212  CMndccmn 19017  Abelcabl 19018

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1916  ax-6 1974  ax-7 2019  ax-8 2115  ax-9 2123  ax-ext 2710

This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1545  df-ex 1787  df-sb 2074  df-clab 2717  df-cleq 2730  df-clel 2811  df-v 3399  df-in 3848  df-ss 3858  df-abl 19020

This theorem is referenced by:  bj-ablssgrpel  35058