Metamath Proof Explorer


Definition df-ogrp

Description: Define class of all ordered groups. An ordered group is a group with a total ordering compatible with its operation. (Contributed by Thierry Arnoux, 13-Mar-2018)

Ref Expression
Assertion df-ogrp oGrp = ( Grp ∩ oMnd )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cogrp oGrp
1 cgrp Grp
2 comnd oMnd
3 1 2 cin ( Grp ∩ oMnd )
4 0 3 wceq oGrp = ( Grp ∩ oMnd )