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Metamath Proof Explorer

Theorem 0dif

Description: The difference between the empty set and a class. Part of Exercise 4.4 of Stoll p. 16. (Contributed by NM, 17-Aug-2004)

		Ref	Expression
	Assertion	0dif	$⊢ \emptyset ∖ A = \emptyset$

Step	Hyp	Ref	Expression
1		difss	$⊢ \emptyset ∖ A \subseteq \emptyset$
2		ss0	$⊢ \emptyset ∖ A \subseteq \emptyset \to \emptyset ∖ A = \emptyset$
3	1 2	ax-mp	$⊢ \emptyset ∖ A = \emptyset$