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Metamath Proof Explorer

Theorem eldisjssi

Description: Subclass theorem for disjoint elementhood, inference version. (Contributed by Peter Mazsa, 28-Sep-2021)

		Ref	Expression
	Hypothesis	eldisjssi.1	$⊢ A \subseteq B$
	Assertion	eldisjssi	$⊢ ElDisj B \to ElDisj A$

Step	Hyp	Ref	Expression
1		eldisjssi.1	$⊢ A \subseteq B$
2		eldisjss	$⊢ A \subseteq B \to (ElDisj B \to ElDisj A)$
3	1 2	ax-mp	$⊢ ElDisj B \to ElDisj A$