Theorem fv2 5634

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.)

Assertion

Ref	Expression
fv2	|- ( F ` A ) = U. { x | A. y ( A F y <-> y = x ) }

Distinct variable groups:   x, y, A   x, F, y

Proof of Theorem fv2

Step	Hyp	Ref	Expression
1		df-fv 5334	. 2 |- ( F ` A ) = ( iota y A F y )
2		dfiota2 5287	. 2 |- ( iota y A F y ) = U. { x | A. y ( A F y <-> y = x ) }
3	1, 2	eqtri 2252	1 |- ( F ` A ) = U. { x | A. y ( A F y <-> y = x ) }

Syntax hints:   <-> wb 105   A.wal 1395   = wceq 1397   {cab 2217   U.cuni 3893   class class class wbr 4088   iotacio 5284   ` cfv 5326

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-rex 2516  df-sn 3675  df-uni 3894  df-iota 5286  df-fv 5334

This theorem is referenced by:  elfv  5637