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Metamath Proof Explorer

Theorem difexd

Description: Existence of a difference. (Contributed by SN, 16-Jul-2024)

		Ref	Expression
	Hypothesis	difexd.1	$⊢ φ \to A \in V$
	Assertion	difexd	$⊢ φ \to A ∖ B \in V$

Step	Hyp	Ref	Expression
1		difexd.1	$⊢ φ \to A \in V$
2		difexg	$⊢ A \in V \to A ∖ B \in V$
3	1 2	syl	$⊢ φ \to A ∖ B \in V$