Theorem disjssd

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

	Ref	Expression
Hypothesis	disjssd.1	$$⊢\phi \to A\subseteq B$$
Assertion	disjssd	$$⊢\phi \to \left(DisjB\to DisjA\right)$$

Proof

Step	Hyp	Ref	Expression
1		disjssd.1	$$⊢\phi \to A\subseteq B$$
2		disjss	$$⊢A\subseteq B\to \left(DisjB\to DisjA\right)$$
3	1 2	syl	$$⊢\phi \to \left(DisjB\to DisjA\right)$$