Theorem ringrngd

Description: A unital ring is a non-unital ring, deduction version. (Contributed by Thierry Arnoux, 15-Feb-2026)

	Ref	Expression
Hypothesis	ringrngd.1	⊢ ( 𝜑 → 𝑅 ∈ Ring )
Assertion	ringrngd	⊢ ( 𝜑 → 𝑅 ∈ Rng )

Proof

Step	Hyp	Ref	Expression
1		ringrngd.1	⊢ ( 𝜑 → 𝑅 ∈ Ring )
2		ringrng	⊢ ( 𝑅 ∈ Ring → 𝑅 ∈ Rng )
3	1 2	syl	⊢ ( 𝜑 → 𝑅 ∈ Rng )