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Theorem fv2 5284
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
StepHypRef Expression
1 df-fv 5010 . 2  |-  ( F `
 A )  =  ( iota y A F y )
2 dfiota2 4968 . 2  |-  ( iota y A F y )  =  U. {
x  |  A. y
( A F y  <-> 
y  =  x ) }
31, 2eqtri 2108 1  |-  ( F `
 A )  = 
U. { x  | 
A. y ( A F y  <->  y  =  x ) }
Colors of variables: wff set class
Syntax hints:    <-> wb 103   A.wal 1287    = wceq 1289   {cab 2074   U.cuni 3648   class class class wbr 3837   iotacio 4965   ` cfv 5002
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rex 2365  df-sn 3447  df-uni 3649  df-iota 4967  df-fv 5010
This theorem is referenced by:  elfv  5287
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