Theorem subrngrcl

Description: Reverse closure for a subring predicate. (Contributed by AV, 14-Feb-2025)

	Ref	Expression
Assertion	subrngrcl	Could not format assertion : No typesetting found for |- ( A e. ( SubRng ` R ) -> R e. Rng ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢{\mathrm{Base}}_R={\mathrm{Base}}_R$$
2	1	issubrng	Could not format ( A e. ( SubRng ` R ) <-> ( R e. Rng /\ ( R |`s A ) e. Rng /\ A C_ ( Base ` R ) ) ) : No typesetting found for |- ( A e. ( SubRng ` R ) <-> ( R e. Rng /\ ( R |`s A ) e. Rng /\ A C_ ( Base ` R ) ) ) with typecode |-
3	2	simp1bi	Could not format ( A e. ( SubRng ` R ) -> R e. Rng ) : No typesetting found for |- ( A e. ( SubRng ` R ) -> R e. Rng ) with typecode |-