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Theorem fveu 5661
Description: The value of a function at a unique point. (Contributed by Scott Fenton, 6-Oct-2017.)
Assertion
Ref Expression
fveu  |-  ( E! x  A F x  ->  ( F `  A )  =  U. { x  |  A F x } )
Distinct variable groups:    x, F    x, A

Proof of Theorem fveu
StepHypRef Expression
1 df-fv 5403 . 2  |-  ( F `
 A )  =  ( iota x A F x )
2 iotauni 5371 . 2  |-  ( E! x  A F x  ->  ( iota x A F x )  = 
U. { x  |  A F x }
)
31, 2syl5eq 2432 1  |-  ( E! x  A F x  ->  ( F `  A )  =  U. { x  |  A F x } )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649   E!weu 2239   {cab 2374   U.cuni 3958   class class class wbr 4154   iotacio 5357   ` cfv 5395
This theorem is referenced by:  afveu  27687
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2369
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2243  df-clab 2375  df-cleq 2381  df-clel 2384  df-nfc 2513  df-rex 2656  df-v 2902  df-sbc 3106  df-un 3269  df-sn 3764  df-pr 3765  df-uni 3959  df-iota 5359  df-fv 5403
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