Theorem simpg2nsg

Description: A simple group has two normal subgroups. (Contributed by Rohan Ridenour, 3-Aug-2023)

	Ref	Expression
Assertion	simpg2nsg	$$⊢G\in \mathrm{SimpGrp}\to \mathrm{NrmSGrp}\left(G\right)\approx 2_{𝑜}$$

Proof

Step	Hyp	Ref	Expression
1		issimpg	$$⊢G\in \mathrm{SimpGrp}\leftrightarrow \left(G\in \mathrm{Grp}\wedge \mathrm{NrmSGrp}\left(G\right)\approx 2_{𝑜}\right)$$
2	1	simprbi	$$⊢G\in \mathrm{SimpGrp}\to \mathrm{NrmSGrp}\left(G\right)\approx 2_{𝑜}$$