Theorem ssd

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

	Ref	Expression
Hypothesis	ssd.1	|- ( ( ph /\ x e. A ) -> x e. B )
Assertion	ssd	|- ( ph -> A C_ B )

Proof

Step	Hyp	Ref	Expression
1		ssd.1	|- ( ( ph /\ x e. A ) -> x e. B )
2		nfv	|- F/ x ph
3	2 1	ssdf	|- ( ph -> A C_ B )