Theorem bj-ablsscmn 33685

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 18549	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss2 4058	. 2 ⊢ (Grp ∩ CMnd) ⊆ CMnd
3	1, 2	eqsstri 3860	1 ⊢ Abel ⊆ CMnd

Syntax hints:   ∩ cin 3797   ⊆ wss 3798  Grpcgrp 17776  CMndccmn 18546  Abelcabl 18547

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-10 2192  ax-11 2207  ax-12 2220  ax-ext 2803

This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-tru 1660  df-ex 1879  df-nf 1883  df-sb 2068  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-v 3416  df-in 3805  df-ss 3812  df-abl 18549

This theorem is referenced by:  bj-ablsscmnel  33686  bj-rrvecsscmn  33697