Theorem bj-ablsscmn 38030

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 19910	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss2 4183	. 2 ⊢ (Grp ∩ CMnd) ⊆ CMnd
3	1, 2	eqsstri 3977	1 ⊢ Abel ⊆ CMnd

This proof depends on syntax axioms:   ∩ cin 3898   ⊆ wss 3899  Grpcgrp 19057  CMndccmn 19907  Abelcabl 19908

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 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-rab 3413  df-v 3452  df-in 3906  df-ss 3916  df-abl 19910

This theorem is used by:  bj-ablsscmnel  38031