Theorem bj-ablsscmn 38467

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 20048	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss2 4137	. 2 ⊢ (Grp ∩ CMnd) ⊆ CMnd
3	1, 2	eqsstri 3959	1 ⊢ Abel ⊆ CMnd

This proof depends on syntax axioms:   ⊆ wss 3900   ∩ cin 4092  Grpcgrp 19194  CMndccmn 20045  Abelcabl 20046

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-rab 3417  df-v 3456  df-ss 3901  df-in 4094  df-abl 20048

This theorem is used by:  bj-ablsscmnel  38468