Theorem pssirr

Description: Proper subclass is irreflexive. Theorem 7 of Suppes p. 23. (Contributed by NM, 7-Feb-1996)

	Ref	Expression
Assertion	pssirr	$$⊢\neg A\subset A$$

Proof

Step	Hyp	Ref	Expression
1		pm3.24	$$⊢\neg \left(A\subseteq A\wedge \neg A\subseteq A\right)$$
2		dfpss3	$$⊢A\subset A\leftrightarrow \left(A\subseteq A\wedge \neg A\subseteq A\right)$$
3	1 2	mtbir	$$⊢\neg A\subset A$$