Theorem bj-ablssgrp 34691

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 18901	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss1 4155	. 2 ⊢ (Grp ∩ CMnd) ⊆ Grp
3	1, 2	eqsstri 3949	1 ⊢ Abel ⊆ Grp

Syntax hints:   ∩ cin 3880   ⊆ wss 3881  Grpcgrp 18095  CMndccmn 18898  Abelcabl 18899

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770

This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-in 3888  df-ss 3898  df-abl 18901

This theorem is referenced by:  bj-ablssgrpel  34692