ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  fv2 Unicode version

Theorem fv2 5201
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 4938 . 2  |-  ( F `
 A )  =  ( iota y A F y )
2 dfiota2 4896 . 2  |-  ( iota y A F y )  =  U. {
x  |  A. y
( A F y  <-> 
y  =  x ) }
31, 2eqtri 2076 1  |-  ( F `
 A )  = 
U. { x  | 
A. y ( A F y  <->  y  =  x ) }
Colors of variables: wff set class
Syntax hints:    <-> wb 102   A.wal 1257    = wceq 1259   {cab 2042   U.cuni 3608   class class class wbr 3792   iotacio 4893   ` cfv 4930
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-sn 3409  df-uni 3609  df-iota 4895  df-fv 4938
This theorem is referenced by:  elfv  5204
  Copyright terms: Public domain W3C validator