Theorem ogrpgrp

Description: A left-ordered group is a group. (Contributed by Thierry Arnoux, 9-Jul-2018)

	Ref	Expression
Assertion	ogrpgrp	$$⊢G\in \mathrm{oGrp}\to G\in \mathrm{Grp}$$

Proof

Step	Hyp	Ref	Expression
1		isogrp	$$⊢G\in \mathrm{oGrp}\leftrightarrow \left(G\in \mathrm{Grp}\wedge G\in \mathrm{oMnd}\right)$$
2	1	simplbi	$$⊢G\in \mathrm{oGrp}\to G\in \mathrm{Grp}$$