Theorem drnggrpd

Description: A division ring is a group (deduction form). (Contributed by SN, 16-May-2024)

	Ref	Expression
Hypothesis	drngringd.1	⊢ ( 𝜑 → 𝑅 ∈ DivRing )
Assertion	drnggrpd	⊢ ( 𝜑 → 𝑅 ∈ Grp )

Proof

Step	Hyp	Ref	Expression
1		drngringd.1	⊢ ( 𝜑 → 𝑅 ∈ DivRing )
2	1	drngringd	⊢ ( 𝜑 → 𝑅 ∈ Ring )
3	2	ringgrpd	⊢ ( 𝜑 → 𝑅 ∈ Grp )