Theorem fveu 5170

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 4910	. 2 |- ( F ` A ) = ( iota x A F x )
2		iotauni 4879	. 2 |- ( E! x A F x -> ( iota x A F x ) = U. { x | A F x } )
3	1, 2	syl5eq 2084	1 |- ( E! x A F x -> ( F ` A ) = U. { x | A F x } )

Syntax hints:   -> wi 4   = wceq 1243   E!weu 1900   {cab 2026   U.cuni 3580   class class class wbr 3764   iotacio 4865   ` cfv 4902

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-sbc 2765  df-un 2922  df-sn 3381  df-pr 3382  df-uni 3581  df-iota 4867  df-fv 4910

This theorem is referenced by: (None)