Theorem pssnssi

Description: A proper subclass does not include the other class. (Contributed by Glauco Siliprandi, 26-Jun-2021)

	Ref	Expression
Hypothesis	pssnssi.1	$$⊢A\subset B$$
Assertion	pssnssi	$$⊢\neg B\subseteq A$$

Proof

Step	Hyp	Ref	Expression
1		pssnssi.1	$$⊢A\subset B$$
2		dfpss3	$$⊢A\subset B\leftrightarrow \left(A\subseteq B\wedge \neg B\subseteq A\right)$$
3	1 2	mpbi	$$⊢\left(A\subseteq B\wedge \neg B\subseteq A\right)$$
4	3	simpri	$$⊢\neg B\subseteq A$$