Theorem bj-ablsscmn 36154

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 19650	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss2 4229	. 2 ⊢ (Grp ∩ CMnd) ⊆ CMnd
3	1, 2	eqsstri 4016	1 ⊢ Abel ⊆ CMnd

Syntax hints:   ∩ cin 3947   ⊆ wss 3948  Grpcgrp 18818  CMndccmn 19647  Abelcabl 19648

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-rab 3433  df-v 3476  df-in 3955  df-ss 3965  df-abl 19650

This theorem is referenced by:  bj-ablsscmnel  36155