Theorem bj-ablssgrp 37234

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 19819	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss1 4258	. 2 ⊢ (Grp ∩ CMnd) ⊆ Grp
3	1, 2	eqsstri 4043	1 ⊢ Abel ⊆ Grp

Syntax hints:   ∩ cin 3975   ⊆ wss 3976  Grpcgrp 18967  CMndccmn 19816  Abelcabl 19817

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-v 3490  df-in 3983  df-ss 3993  df-abl 19819

This theorem is referenced by:  bj-ablssgrpel  37235