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Theorem fveu 5711
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 5453 . 2  |-  ( F `
 A )  =  ( iota x A F x )
2 iotauni 5421 . 2  |-  ( E! x  A F x  ->  ( iota x A F x )  = 
U. { x  |  A F x }
)
31, 2syl5eq 2479 1  |-  ( E! x  A F x  ->  ( F `  A )  =  U. { x  |  A F x } )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652   E!weu 2280   {cab 2421   U.cuni 4007   class class class wbr 4204   iotacio 5407   ` cfv 5445
This theorem is referenced by:  afveu  27931
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rex 2703  df-v 2950  df-sbc 3154  df-un 3317  df-sn 3812  df-pr 3813  df-uni 4008  df-iota 5409  df-fv 5453
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