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 ) = U. { x | A. y ( A F y <-> y = x ) }

Proof

Step	Hyp	Ref	Expression
1		df-fv	|- ( F ` A ) = ( iota y A F y )
2		dfiota2	|- ( iota y A F y ) = U. { x | A. y ( A F y <-> y = x ) }
3	1 2	eqtri	|- ( F ` A ) = U. { x | A. y ( A F y <-> y = x ) }