Theorem fv2 5409

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 5126	. 2 |- ( F ` A ) = ( iota y A F y )
2		dfiota2 5084	. 2 |- ( iota y A F y ) = U. { x | A. y ( A F y <-> y = x ) }
3	1, 2	eqtri 2158	1 |- ( F ` A ) = U. { x | A. y ( A F y <-> y = x ) }

Syntax hints:   <-> wb 104   A.wal 1329   = wceq 1331   {cab 2123   U.cuni 3731   class class class wbr 3924   iotacio 5081   ` cfv 5118

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rex 2420  df-sn 3528  df-uni 3732  df-iota 5083  df-fv 5126

This theorem is referenced by:  elfv  5412