Theorem pssirr

Description: Proper subclass is irreflexive. Theorem 7 of Suppes p. 23. (Contributed by NM, 7-Feb-1996) (Proof shortened by Umit Teoman Dogan, 10-Jun-2026)

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

Proof

Step	Hyp	Ref	Expression
1		neirr	$$⊢\neg A\ne A$$
2		pssne	$$⊢A\subset A\to A\ne A$$
3	1 2	mto	$$⊢\neg A\subset A$$