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Metamath Proof Explorer

Theorem difexg

Description: Existence of a difference. (Contributed by NM, 26-May-1998)

		Ref	Expression
	Assertion	difexg	$⊢ A \in V \to A ∖ B \in V$

Step	Hyp	Ref	Expression
1		difss	$⊢ A ∖ B \subseteq A$
2		ssexg	$⊢ (A ∖ B \subseteq A \land A \in V) \to A ∖ B \in V$
3	1 2	mpan	$⊢ A \in V \to A ∖ B \in V$