Theorem simpggrpd

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

	Ref	Expression
Hypothesis	simpggrpd.1	⊢ ( 𝜑 → 𝐺 ∈ SimpGrp )
Assertion	simpggrpd	⊢ ( 𝜑 → 𝐺 ∈ Grp )

Proof

Step	Hyp	Ref	Expression
1		simpggrpd.1	⊢ ( 𝜑 → 𝐺 ∈ SimpGrp )
2		simpggrp	⊢ ( 𝐺 ∈ SimpGrp → 𝐺 ∈ Grp )
3	1 2	syl	⊢ ( 𝜑 → 𝐺 ∈ Grp )