Theorem bj-ablssgrp 37953

Description: Abelian groups are groups. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-ablssgrp	⊢ Abel ⊆ Grp

Proof of Theorem bj-ablssgrp

Step	Hyp	Ref	Expression
1		df-abl 19877	. 2 ⊢ Abel = (Grp ∩ CMnd)
2		inss1 4189	. 2 ⊢ (Grp ∩ CMnd) ⊆ Grp
3	1, 2	eqsstri 3984	1 ⊢ Abel ⊆ Grp

This proof depends on syntax axioms:   ∩ cin 3905   ⊆ wss 3906  Grpcgrp 19024  CMndccmn 19874  Abelcabl 19875

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 2148  ax-9 2156  ax-ext 2737

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459  df-in 3913  df-ss 3923  df-abl 19877

This theorem is used by:  bj-ablssgrpel  37954