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Theorem fveu 5755
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 5497 . 2  |-  ( F `
 A )  =  ( iota x A F x )
2 iotauni 5465 . 2  |-  ( E! x  A F x  ->  ( iota x A F x )  = 
U. { x  |  A F x }
)
31, 2syl5eq 2487 1  |-  ( E! x  A F x  ->  ( F `  A )  =  U. { x  |  A F x } )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1654   E!weu 2288   {cab 2429   U.cuni 4044   class class class wbr 4243   iotacio 5451   ` cfv 5489
This theorem is referenced by:  afveu  28105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-eu 2292  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-rex 2718  df-v 2967  df-sbc 3171  df-un 3314  df-sn 3849  df-pr 3850  df-uni 4045  df-iota 5453  df-fv 5497
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