Theorem fv2 5193

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 4930	. 2 |- ( F ` A ) = ( iota y A F y )
2		dfiota2 4888	. 2 |- ( iota y A F y ) = U. { x | A. y ( A F y <-> y = x ) }
3	1, 2	eqtri 2101	1 |- ( F ` A ) = U. { x | A. y ( A F y <-> y = x ) }

Syntax hints:   <-> wb 103   A.wal 1282   = wceq 1284   {cab 2067   U.cuni 3601   class class class wbr 3785   iotacio 4885   ` cfv 4922

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-rex 2354  df-sn 3404  df-uni 3602  df-iota 4887  df-fv 4930

This theorem is referenced by:  elfv  5196