Theorem bj-ablsscmn 36813

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 19740	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss2 4224	. 2 ⊢ (Grp ∩ CMnd) ⊆ CMnd
3	1, 2	eqsstri 4007	1 ⊢ Abel ⊆ CMnd

Syntax hints:   ∩ cin 3939   ⊆ wss 3940  Grpcgrp 18892  CMndccmn 19737  Abelcabl 19738

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696

This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-rab 3420  df-v 3465  df-in 3947  df-ss 3957  df-abl 19740

This theorem is referenced by:  bj-ablsscmnel  36814