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Theorem fv2 5116
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 `

U. {  |  F  }
Distinct variable groups:   ,,   , F,

Proof of Theorem fv2
StepHypRef Expression
1 df-fv 4853 . 2  F `
 iota F
2 dfiota2 4811 . 2  iota F  U. {  |  F  }
31, 2eqtri 2057 1  F `

U. {  |  F  }
Colors of variables: wff set class
Syntax hints:   wb 98  wal 1240   wceq 1242   {cab 2023   U.cuni 3571   class class class wbr 3755   iotacio 4808   ` cfv 4845
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-sn 3373  df-uni 3572  df-iota 4810  df-fv 4853
This theorem is referenced by:  elfv  5119
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