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Metamath Proof Explorer

Theorem nelss

Description: Demonstrate by witnesses that two classes lack a subclass relation. (Contributed by Stefan O'Rear, 5-Feb-2015)

		Ref	Expression
	Assertion	nelss	$⊢ (A \in B \land \neg A \in C) \to \neg B \subseteq C$

Step	Hyp	Ref	Expression
1		ssel	$⊢ B \subseteq C \to (A \in B \to A \in C)$
2	1	com12	$⊢ A \in B \to (B \subseteq C \to A \in C)$
3	2	con3dimp	$⊢ (A \in B \land \neg A \in C) \to \neg B \subseteq C$