Theorem bj-ablsscmn 37242

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 19762	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss2 4213	. 2 ⊢ (Grp ∩ CMnd) ⊆ CMnd
3	1, 2	eqsstri 4005	1 ⊢ Abel ⊆ CMnd

Syntax hints:   ∩ cin 3925   ⊆ wss 3926  Grpcgrp 18914  CMndccmn 19759  Abelcabl 19760

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2714  df-cleq 2727  df-clel 2809  df-rab 3416  df-v 3461  df-in 3933  df-ss 3943  df-abl 19762

This theorem is referenced by:  bj-ablsscmnel  37243