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	$$⊢\phi \to A\subseteq B$$
Assertion	ssneld	$$⊢\phi \to \left(\neg C\in B\to \neg C\in A\right)$$

Proof

Step	Hyp	Ref	Expression
1		ssneld.1	$$⊢\phi \to A\subseteq B$$
2	1	sseld	$$⊢\phi \to \left(C\in A\to C\in B\right)$$
3	2	con3d	$$⊢\phi \to \left(\neg C\in B\to \neg C\in A\right)$$