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Theorem fveu 6881
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 6551 . 2 (𝐹𝐴) = (℩𝑥𝐴𝐹𝑥)
2 iotauni 6518 . 2 (∃!𝑥 𝐴𝐹𝑥 → (℩𝑥𝐴𝐹𝑥) = {𝑥𝐴𝐹𝑥})
31, 2eqtrid 2780 1 (∃!𝑥 𝐴𝐹𝑥 → (𝐹𝐴) = {𝑥𝐴𝐹𝑥})
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1534  ∃!weu 2558  {cab 2705   cuni 4904   class class class wbr 5143  cio 6493  cfv 6543
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-10 2130  ax-12 2167  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-tru 1537  df-ex 1775  df-nf 1779  df-sb 2061  df-mo 2530  df-eu 2559  df-clab 2706  df-cleq 2720  df-clel 2806  df-v 3472  df-un 3950  df-in 3952  df-ss 3962  df-sn 4626  df-pr 4628  df-uni 4905  df-iota 6495  df-fv 6551
This theorem is referenced by:  afveu  46524
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