Theorem bj-ablsscmn 37805

Description: Abelian groups are commutative monoids. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-ablsscmn	⊢ Abel ⊆ CMnd

Proof of Theorem bj-ablsscmn

Step	Hyp	Ref	Expression
1		df-abl 19849	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss2 4198	. 2 ⊢ (Grp ∩ CMnd) ⊆ CMnd
3	1, 2	eqsstri 3991	1 ⊢ Abel ⊆ CMnd

Syntax hints:   ∩ cin 3912   ⊆ wss 3913  Grpcgrp 18996  CMndccmn 19846  Abelcabl 19847

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1570  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-rab 3424  df-v 3465  df-in 3920  df-ss 3930  df-abl 19849

This theorem is referenced by:  bj-ablsscmnel  37806