Theorem eldisjssd

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

	Ref	Expression
Hypothesis	eldisjssd.1	$$⊢\phi \to A\subseteq B$$
Assertion	eldisjssd	$$⊢\phi \to \left(ElDisjB\to ElDisjA\right)$$

Proof

Step	Hyp	Ref	Expression
1		eldisjssd.1	$$⊢\phi \to A\subseteq B$$
2		eldisjss	$$⊢A\subseteq B\to \left(ElDisjB\to ElDisjA\right)$$
3	1 2	syl	$$⊢\phi \to \left(ElDisjB\to ElDisjA\right)$$