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	⊢ ¬ 𝐴 ⊊ 𝐴

Proof

Step	Hyp	Ref	Expression
1		neirr	⊢ ¬ 𝐴 ≠ 𝐴
2		pssne	⊢ ( 𝐴 ⊊ 𝐴 → 𝐴 ≠ 𝐴 )
3	1 2	mto	⊢ ¬ 𝐴 ⊊ 𝐴