Theorem simpggrpd

Description: A simple group is a group. (Contributed by Rohan Ridenour, 3-Aug-2023)

	Ref	Expression
Hypothesis	simpggrpd.1	$$⊢\phi \to G\in \mathrm{SimpGrp}$$
Assertion	simpggrpd	$$⊢\phi \to G\in \mathrm{Grp}$$

Proof

Step	Hyp	Ref	Expression
1		simpggrpd.1	$$⊢\phi \to G\in \mathrm{SimpGrp}$$
2		simpggrp	$$⊢G\in \mathrm{SimpGrp}\to G\in \mathrm{Grp}$$
3	1 2	syl	$$⊢\phi \to G\in \mathrm{Grp}$$