Definition df-simpg 19206

Description: Define class of all simple groups. A simple group is a group (df-grp 18099) with exactly two normal subgroups. These are always the subgroup of all elements and the subgroup containing only the identity (simpgnsgbid 19218). (Contributed by Rohan Ridenour, 3-Aug-2023.)

Assertion

Ref	Expression
df-simpg	⊢ SimpGrp = {𝑔 ∈ Grp ∣ (NrmSGrp‘𝑔) ≈ 2o}

Detailed syntax breakdown of Definition df-simpg

Step	Hyp	Ref	Expression
1		csimpg 19205	. 2 class SimpGrp
2		vg	. . . . . 6 setvar 𝑔
3	2	cv 1535	. . . . 5 class 𝑔
4		cnsg 18267	. . . . 5 class NrmSGrp
5	3, 4	cfv 6348	. . . 4 class (NrmSGrp‘𝑔)
6		c2o 8089	. . . 4 class 2o
7		cen 8499	. . . 4 class ≈
8	5, 6, 7	wbr 5059	. . 3 wff (NrmSGrp‘𝑔) ≈ 2o
9		cgrp 18096	. . 3 class Grp
10	8, 2, 9	crab 3141	. 2 class {𝑔 ∈ Grp ∣ (NrmSGrp‘𝑔) ≈ 2o}
11	1, 10	wceq 1536	1 wff SimpGrp = {𝑔 ∈ Grp ∣ (NrmSGrp‘𝑔) ≈ 2o}

This definition is referenced by:  issimpg  19207