Theorem bj-ablsscmn 36680

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 19722	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss2 4225	. 2 ⊢ (Grp ∩ CMnd) ⊆ CMnd
3	1, 2	eqsstri 4012	1 ⊢ Abel ⊆ CMnd

Syntax hints:   ∩ cin 3943   ⊆ wss 3944  Grpcgrp 18875  CMndccmn 19719  Abelcabl 19720

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 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2698

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2705  df-cleq 2719  df-clel 2805  df-rab 3428  df-v 3471  df-in 3951  df-ss 3961  df-abl 19722

This theorem is referenced by:  bj-ablsscmnel  36681