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Metamath Proof Explorer

Theorem fv2

Description: Alternate definition of function value. Definition 10.11 of Quine p. 68. (Contributed by NM, 30-Apr-2004) (Proof shortened by Andrew Salmon, 17-Sep-2011) (Revised by Mario Carneiro, 31-Aug-2015)

		Ref	Expression
	Assertion	fv2	$⊢ F (A) = ⋃ \{x \| \forall y (A F y \leftrightarrow y = x)\}$

Proof

Step	Hyp	Ref	Expression
1		df-fv	$⊢ F (A) = (ι y \| A F y)$
2		dfiota2	$⊢ (ι y \| A F y) = ⋃ \{x \| \forall y (A F y \leftrightarrow y = x)\}$
3	1 2	eqtri	$⊢ F (A) = ⋃ \{x \| \forall y (A F y \leftrightarrow y = x)\}$