Theorem fveu 5460

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 5178	. 2 |- ( F ` A ) = ( iota x A F x )
2		iotauni 5147	. 2 |- ( E! x A F x -> ( iota x A F x ) = U. { x | A F x } )
3	1, 2	syl5eq 2202	1 |- ( E! x A F x -> ( F ` A ) = U. { x | A F x } )

Syntax hints:   -> wi 4   = wceq 1335   E!weu 2006   {cab 2143   U.cuni 3772   class class class wbr 3965   iotacio 5133   ` cfv 5170

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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139

This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-eu 2009  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-rex 2441  df-v 2714  df-sbc 2938  df-un 3106  df-sn 3566  df-pr 3567  df-uni 3773  df-iota 5135  df-fv 5178

This theorem is referenced by: (None)