Theorem bj-ablsscmn 35458

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 19400	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss2 4169	. 2 ⊢ (Grp ∩ CMnd) ⊆ CMnd
3	1, 2	eqsstri 3960	1 ⊢ Abel ⊆ CMnd

Syntax hints:   ∩ cin 3891   ⊆ wss 3892  Grpcgrp 18588  CMndccmn 19397  Abelcabl 19398

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2015  ax-8 2112  ax-9 2120  ax-ext 2711

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1545  df-ex 1787  df-sb 2072  df-clab 2718  df-cleq 2732  df-clel 2818  df-rab 3075  df-v 3433  df-in 3899  df-ss 3909  df-abl 19400

This theorem is referenced by:  bj-ablsscmnel  35459