Theorem bj-ablssgrp 36146

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 19646	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss1 4228	. 2 ⊢ (Grp ∩ CMnd) ⊆ Grp
3	1, 2	eqsstri 4016	1 ⊢ Abel ⊆ Grp

Syntax hints:   ∩ cin 3947   ⊆ wss 3948  Grpcgrp 18816  CMndccmn 19643  Abelcabl 19644

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-in 3955  df-ss 3965  df-abl 19646

This theorem is referenced by:  bj-ablssgrpel  36147