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Theorem fveu 6150
 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 5865 . 2 (𝐹𝐴) = (℩𝑥𝐴𝐹𝑥)
2 iotauni 5832 . 2 (∃!𝑥 𝐴𝐹𝑥 → (℩𝑥𝐴𝐹𝑥) = {𝑥𝐴𝐹𝑥})
31, 2syl5eq 2667 1 (∃!𝑥 𝐴𝐹𝑥 → (𝐹𝐴) = {𝑥𝐴𝐹𝑥})
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1480  ∃!weu 2469  {cab 2607  ∪ cuni 4409   class class class wbr 4623  ℩cio 5818  ‘cfv 5857 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-eu 2473  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-rex 2914  df-v 3192  df-sbc 3423  df-un 3565  df-sn 4156  df-pr 4158  df-uni 4410  df-iota 5820  df-fv 5865 This theorem is referenced by:  afveu  40567
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