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Metamath Proof Explorer

Theorem ssnpss

Description: Partial trichotomy law for subclasses. (Contributed by NM, 16-May-1996) (Proof shortened by Andrew Salmon, 26-Jun-2011)

		Ref	Expression
	Assertion	ssnpss	$⊢ A \subseteq B \to \neg B \subset A$

Step	Hyp	Ref	Expression
1		dfpss3	$⊢ B \subset A \leftrightarrow (B \subseteq A \land \neg A \subseteq B)$
2	1	simprbi	$⊢ B \subset A \to \neg A \subseteq B$
3	2	con2i	$⊢ A \subseteq B \to \neg B \subset A$