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Theorem fveu 5840
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 5576 . 2  |-  ( F `
 A )  =  ( iota x A F x )
2 iotauni 5544 . 2  |-  ( E! x  A F x  ->  ( iota x A F x )  = 
U. { x  |  A F x }
)
31, 2syl5eq 2455 1  |-  ( E! x  A F x  ->  ( F `  A )  =  U. { x  |  A F x } )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1405   E!weu 2238   {cab 2387   U.cuni 4190   class class class wbr 4394   iotacio 5530   ` cfv 5568
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-eu 2242  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-rex 2759  df-v 3060  df-sbc 3277  df-un 3418  df-sn 3972  df-pr 3974  df-uni 4191  df-iota 5532  df-fv 5576
This theorem is referenced by:  afveu  37587
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