Theorem fveu 5631

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 5334	. 2 |- ( F ` A ) = ( iota x A F x )
2		iotauni 5299	. 2 |- ( E! x A F x -> ( iota x A F x ) = U. { x | A F x } )
3	1, 2	eqtrid 2276	1 |- ( E! x A F x -> ( F ` A ) = U. { x | A F x } )

Syntax hints:   -> wi 4   = wceq 1397   E!weu 2079   {cab 2217   U.cuni 3893   class class class wbr 4088   iotacio 5284   ` cfv 5326

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-eu 2082  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-rex 2516  df-v 2804  df-sbc 3032  df-un 3204  df-sn 3675  df-pr 3676  df-uni 3894  df-iota 5286  df-fv 5334

This theorem is referenced by: (None)