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Metamath Proof Explorer

Theorem fveu

Description: The value of a function at a unique point. (Contributed by Scott Fenton, 6-Oct-2017)

		Ref	Expression
	Assertion	fveu	$⊢ \exists! x A F x \to F (A) = ⋃ \{x \| A F x\}$

Step	Hyp	Ref	Expression
1		df-fv	$⊢ F (A) = (ι x \| A F x)$
2		iotauni	$⊢ \exists! x A F x \to (ι x \| A F x) = ⋃ \{x \| A F x\}$
3	1 2	eqtrid	$⊢ \exists! x A F x \to F (A) = ⋃ \{x \| A F x\}$