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Theorem fv2 6173
 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 5884 . 2 (𝐹𝐴) = (℩𝑦𝐴𝐹𝑦)
2 dfiota2 5840 . 2 (℩𝑦𝐴𝐹𝑦) = {𝑥 ∣ ∀𝑦(𝐴𝐹𝑦𝑦 = 𝑥)}
31, 2eqtri 2642 1 (𝐹𝐴) = {𝑥 ∣ ∀𝑦(𝐴𝐹𝑦𝑦 = 𝑥)}
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 196  ∀wal 1479   = wceq 1481  {cab 2606  ∪ cuni 4427   class class class wbr 4644  ℩cio 5837  ‘cfv 5876 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-rex 2915  df-sn 4169  df-uni 4428  df-iota 5839  df-fv 5884 This theorem is referenced by:  elfv  6176
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