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Theorem fveu 6896
Description: The value of a function at a unique point. (Contributed by Scott Fenton, 6-Oct-2017.)
Assertion
Ref Expression
fveu (∃!𝑥 𝐴𝐹𝑥 → (𝐹𝐴) = {𝑥𝐴𝐹𝑥})
Distinct variable groups:   𝑥,𝐹   𝑥,𝐴

Proof of Theorem fveu
StepHypRef Expression
1 df-fv 6571 . 2 (𝐹𝐴) = (℩𝑥𝐴𝐹𝑥)
2 iotauni 6538 . 2 (∃!𝑥 𝐴𝐹𝑥 → (℩𝑥𝐴𝐹𝑥) = {𝑥𝐴𝐹𝑥})
31, 2eqtrid 2787 1 (∃!𝑥 𝐴𝐹𝑥 → (𝐹𝐴) = {𝑥𝐴𝐹𝑥})
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1537  ∃!weu 2566  {cab 2712   cuni 4912   class class class wbr 5148  cio 6514  cfv 6563
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-12 2175  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-nf 1781  df-sb 2063  df-mo 2538  df-eu 2567  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-un 3968  df-ss 3980  df-sn 4632  df-pr 4634  df-uni 4913  df-iota 6516  df-fv 6571
This theorem is referenced by:  afveu  47103
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