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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 (𝐹𝐴) = {𝑥 ∣ ∀𝑦(𝐴𝐹𝑦𝑦 = 𝑥)}
Distinct variable groups:   𝑥,𝑦,𝐴   𝑥,𝐹,𝑦

Proof of Theorem fv2
StepHypRef Expression
1 df-fv 5010 . 2 (𝐹𝐴) = (℩𝑦𝐴𝐹𝑦)
2 dfiota2 4968 . 2 (℩𝑦𝐴𝐹𝑦) = {𝑥 ∣ ∀𝑦(𝐴𝐹𝑦𝑦 = 𝑥)}
31, 2eqtri 2108 1 (𝐹𝐴) = {𝑥 ∣ ∀𝑦(𝐴𝐹𝑦𝑦 = 𝑥)}
Colors of variables: wff set class
Syntax hints:  wb 103  wal 1287   = wceq 1289  {cab 2074   cuni 3648   class class class wbr 3837  cio 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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