Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-ablssgrp Structured version   Unicode version

Theorem bj-ablssgrp 32670
Description: Abelian groups are groups. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-ablssgrp  |-  Abel  C_  Grp

Proof of Theorem bj-ablssgrp
StepHypRef Expression
1 df-abl 16301 . 2  |-  Abel  =  ( Grp  i^i CMnd )
2 inss1 3591 . 2  |-  ( Grp 
i^i CMnd )  C_  Grp
31, 2eqsstri 3407 1  |-  Abel  C_  Grp
Colors of variables: wff setvar class
Syntax hints:    i^i cin 3348    C_ wss 3349   Grpcgrp 15431  CMndccmn 16298   Abelcabel 16299
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2577  df-v 2995  df-in 3356  df-ss 3363  df-abl 16301
This theorem is referenced by:  bj-ablssgrpel  32671
  Copyright terms: Public domain W3C validator