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	$$⊢\phi \to R\in \mathrm{Ring}$$
Assertion	ringrngd	$$⊢\phi \to R\in \mathrm{Rng}$$

Proof

Step	Hyp	Ref	Expression
1		ringrngd.1	$$⊢\phi \to R\in \mathrm{Ring}$$
2		ringrng	$$⊢R\in \mathrm{Ring}\to R\in \mathrm{Rng}$$
3	1 2	syl	$$⊢\phi \to R\in \mathrm{Rng}$$