Metamath Proof Explorer


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 B
Assertion pssnssi ¬ B A

Proof

Step Hyp Ref Expression
1 pssnssi.1 A B
2 dfpss3 A B A B ¬ B A
3 1 2 mpbi A B ¬ B A
4 3 simpri ¬ B A