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

Theorem bj-ablssgrp 33268
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
StepHypRef Expression
1 df-abl 18242 . 2 Abel = (Grp ∩ CMnd)
2 inss1 3866 . 2 (Grp ∩ CMnd) ⊆ Grp
31, 2eqsstri 3668 1 Abel ⊆ Grp
Colors of variables: wff setvar class
Syntax hints:  cin 3606  wss 3607  Grpcgrp 17469  CMndccmn 18239  Abelcabl 18240
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-v 3233  df-in 3614  df-ss 3621  df-abl 18242
This theorem is referenced by:  bj-ablssgrpel  33269
  Copyright terms: Public domain W3C validator