Theorem bj-ablssgrp 35374

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 19304	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss1 4159	. 2 ⊢ (Grp ∩ CMnd) ⊆ Grp
3	1, 2	eqsstri 3951	1 ⊢ Abel ⊆ Grp

Syntax hints:   ∩ cin 3882   ⊆ wss 3883  Grpcgrp 18492  CMndccmn 19301  Abelcabl 19302

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-in 3890  df-ss 3900  df-abl 19304

This theorem is referenced by:  bj-ablssgrpel  35375