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Metamath Proof Explorer

Theorem predexg

Description: The predecessor class exists when A does. (Contributed by Scott Fenton, 8-Feb-2011) Generalize to closed form. (Revised by BJ, 27-Oct-2024)

		Ref	Expression
	Assertion	predexg	$⊢ A \in V \to Pred (R, A, X) \in V$

Proof

Step	Hyp	Ref	Expression
1		df-pred	$⊢ Pred (R, A, X) = A \cap R^{-1} [\{X\}]$
2		inex1g	$⊢ A \in V \to A \cap R^{-1} [\{X\}] \in V$
3	1 2	eqeltrid	$⊢ A \in V \to Pred (R, A, X) \in V$