Theorem fveu 5281

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

Step	Hyp	Ref	Expression
1		df-fv 5010	. 2 |- ( F ` A ) = ( iota x A F x )
2		iotauni 4979	. 2 |- ( E! x A F x -> ( iota x A F x ) = U. { x | A F x } )
3	1, 2	syl5eq 2132	1 |- ( E! x A F x -> ( F ` A ) = U. { x | A F x } )

Syntax hints:   -> wi 4   = wceq 1289   E!weu 1948   {cab 2074   U.cuni 3648   class class class wbr 3837   iotacio 4965   ` cfv 5002

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-eu 1951  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rex 2365  df-v 2621  df-sbc 2839  df-un 3001  df-sn 3447  df-pr 3448  df-uni 3649  df-iota 4967  df-fv 5010

This theorem is referenced by: (None)