Theorem bj-ablsscmn 37221

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 19801	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss2 4246	. 2 ⊢ (Grp ∩ CMnd) ⊆ CMnd
3	1, 2	eqsstri 4030	1 ⊢ Abel ⊆ CMnd

Syntax hints:   ∩ cin 3962   ⊆ wss 3963  Grpcgrp 18949  CMndccmn 19798  Abelcabl 19799

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1963  ax-7 2003  ax-8 2106  ax-9 2114  ax-ext 2704

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1538  df-ex 1775  df-sb 2061  df-clab 2711  df-cleq 2725  df-clel 2812  df-rab 3433  df-v 3479  df-in 3970  df-ss 3980  df-abl 19801

This theorem is referenced by:  bj-ablsscmnel  37222