Theorem simpg2nsg

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

	Ref	Expression
Assertion	simpg2nsg	⊢ ( 𝐺 ∈ SimpGrp → ( NrmSGrp ‘ 𝐺 ) ≈ 2o )

Proof

Step	Hyp	Ref	Expression
1		issimpg	⊢ ( 𝐺 ∈ SimpGrp ↔ ( 𝐺 ∈ Grp ∧ ( NrmSGrp ‘ 𝐺 ) ≈ 2o ) )
2	1	simprbi	⊢ ( 𝐺 ∈ SimpGrp → ( NrmSGrp ‘ 𝐺 ) ≈ 2o )