Theorem bj-ablsscmn 38308

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 20006	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss2 4133	. 2 ⊢ (Grp ∩ CMnd) ⊆ CMnd
3	1, 2	eqsstri 3955	1 ⊢ Abel ⊆ CMnd

This proof depends on syntax axioms:   ⊆ wss 3896   ∩ cin 4088  Grpcgrp 19153  CMndccmn 20003  Abelcabl 20004

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-rab 3413  df-v 3452  df-ss 3897  df-in 4090  df-abl 20006

This theorem is used by:  bj-ablsscmnel  38309