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Metamath Proof Explorer

Theorem eldisjsim2

Description: An element of the class of disjoint relations is an element of the class of relations. (Contributed by Peter Mazsa, 11-Feb-2026)

		Ref	Expression
	Assertion	eldisjsim2	$⊢ R \in Disjs \to R \in Rels$

Step	Hyp	Ref	Expression
1		elinel2	$⊢ R \in (Disjss \cap Rels) \to R \in Rels$
2		df-disjs	$⊢ Disjs = Disjss \cap Rels$
3	1 2	eleq2s	$⊢ R \in Disjs \to R \in Rels$