Theorem bj-ablsscmn 37731

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 19814	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss2 4187	. 2 ⊢ (Grp ∩ CMnd) ⊆ CMnd
3	1, 2	eqsstri 3980	1 ⊢ Abel ⊆ CMnd

Syntax hints:   ∩ cin 3901   ⊆ wss 3902  Grpcgrp 18966  CMndccmn 19811  Abelcabl 19812

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-ext 2733

This theorem depends on definitions:  df-bi 209  df-an 400  df-tru 1562  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-rab 3414  df-v 3455  df-in 3909  df-ss 3919  df-abl 19814

This theorem is referenced by:  bj-ablsscmnel  37732