Theorem subrngss

Description: A subring is a subset. (Contributed by AV, 14-Feb-2025)

	Ref	Expression
Hypothesis	subrngss.1	$$⊢B={\mathrm{Base}}_R$$
Assertion	subrngss	Could not format assertion : No typesetting found for |- ( A e. ( SubRng ` R ) -> A C_ B ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		subrngss.1	$$⊢B={\mathrm{Base}}_R$$
2	1	issubrng	Could not format ( A e. ( SubRng ` R ) <-> ( R e. Rng /\ ( R |`s A ) e. Rng /\ A C_ B ) ) : No typesetting found for |- ( A e. ( SubRng ` R ) <-> ( R e. Rng /\ ( R |`s A ) e. Rng /\ A C_ B ) ) with typecode |-
3	2	simp3bi	Could not format ( A e. ( SubRng ` R ) -> A C_ B ) : No typesetting found for |- ( A e. ( SubRng ` R ) -> A C_ B ) with typecode |-