Theorem ssd

Description: A sufficient condition for a subclass relationship. (Contributed by Glauco Siliprandi, 3-Jan-2021)

	Ref	Expression
Hypothesis	ssd.1	$$⊢\left(\phi \wedge x\in A\right)\to x\in B$$
Assertion	ssd	$$⊢\phi \to A\subseteq B$$

Proof

Step	Hyp	Ref	Expression
1		ssd.1	$$⊢\left(\phi \wedge x\in A\right)\to x\in B$$
2		nfv	$$⊢Ⅎx\phi$$
3	2 1	ssdf	$$⊢\phi \to A\subseteq B$$