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Metamath Proof Explorer

Theorem slotfn

Description: A slot is a function on sets, treated as structures. (Contributed by Mario Carneiro, 22-Sep-2015)

		Ref	Expression
	Hypothesis	strfvnd.c	$⊢ E = Slot N$
	Assertion	slotfn	$⊢ E Fn V$

Step	Hyp	Ref	Expression
1		strfvnd.c	$⊢ E = Slot N$
2		fvex	$⊢ x (N) \in V$
3		df-slot	$⊢ Slot N = (x \in V ⟼ x (N))$
4	1 3	eqtri	$⊢ E = (x \in V ⟼ x (N))$
5	2 4	fnmpti	$⊢ E Fn V$