Theorem bj-ablssgrp 37528

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 19724	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss1 4191	. 2 ⊢ (Grp ∩ CMnd) ⊆ Grp
3	1, 2	eqsstri 3982	1 ⊢ Abel ⊆ Grp

Syntax hints:   ∩ cin 3902   ⊆ wss 3903  Grpcgrp 18875  CMndccmn 19721  Abelcabl 19722

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 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-v 3444  df-in 3910  df-ss 3920  df-abl 19724

This theorem is referenced by:  bj-ablssgrpel  37529