Theorem bj-ablssgrp 37271

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 19720	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss1 4203	. 2 ⊢ (Grp ∩ CMnd) ⊆ Grp
3	1, 2	eqsstri 3996	1 ⊢ Abel ⊆ Grp

Syntax hints:   ∩ cin 3916   ⊆ wss 3917  Grpcgrp 18872  CMndccmn 19717  Abelcabl 19718

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-v 3452  df-in 3924  df-ss 3934  df-abl 19720

This theorem is referenced by:  bj-ablssgrpel  37272