Theorem ssnel

Description: If not element of a set, then not element of a subset. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Assertion	ssnel	$$⊢\left(A\subseteq B\wedge \neg C\in B\right)\to \neg C\in A$$

Proof

Step	Hyp	Ref	Expression
1		ssel2	$$⊢\left(A\subseteq B\wedge C\in A\right)\to C\in B$$
2	1	stoic1a	$$⊢\left(A\subseteq B\wedge \neg C\in B\right)\to \neg C\in A$$