Theorem ssneld

Description: If a class is not in another class, it is also not in a subclass of that class. Deduction form. (Contributed by David Moews, 1-May-2017)

	Ref	Expression
Hypothesis	ssneld.1	|- ( ph -> A C_ B )
Assertion	ssneld	|- ( ph -> ( -. C e. B -> -. C e. A ) )

Proof

Step	Hyp	Ref	Expression
1		ssneld.1	|- ( ph -> A C_ B )
2	1	sseld	|- ( ph -> ( C e. A -> C e. B ) )
3	2	con3d	|- ( ph -> ( -. C e. B -> -. C e. A ) )