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Theorem bj-ablssgrp 34755
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 16927 . 2  |-  Abel  =  ( Grp  i^i CMnd )
2 inss1 3714 . 2  |-  ( Grp 
i^i CMnd )  C_  Grp
31, 2eqsstri 3529 1  |-  Abel  C_  Grp
Colors of variables: wff setvar class
Syntax hints:    i^i cin 3470    C_ wss 3471   Grpcgrp 16179  CMndccmn 16924   Abelcabl 16925
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-in 3478  df-ss 3485  df-abl 16927
This theorem is referenced by:  bj-ablssgrpel  34756
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