Metamath Proof Explorer


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