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Theorem fveu 5379
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 5099 . 2  |-  ( F `
 A )  =  ( iota x A F x )
2 iotauni 5068 . 2  |-  ( E! x  A F x  ->  ( iota x A F x )  = 
U. { x  |  A F x }
)
31, 2syl5eq 2160 1  |-  ( E! x  A F x  ->  ( F `  A )  =  U. { x  |  A F x } )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1314   E!weu 1975   {cab 2101   U.cuni 3704   class class class wbr 3897   iotacio 5054   ` cfv 5091
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-eu 1978  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-rex 2397  df-v 2660  df-sbc 2881  df-un 3043  df-sn 3501  df-pr 3502  df-uni 3705  df-iota 5056  df-fv 5099
This theorem is referenced by: (None)
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