Theorem fveu 5550

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 5266	. 2 |- ( F ` A ) = ( iota x A F x )
2		iotauni 5231	. 2 |- ( E! x A F x -> ( iota x A F x ) = U. { x | A F x } )
3	1, 2	eqtrid 2241	1 |- ( E! x A F x -> ( F ` A ) = U. { x | A F x } )

Syntax hints:   -> wi 4   = wceq 1364   E!weu 2045   {cab 2182   U.cuni 3839   class class class wbr 4033   iotacio 5217   ` cfv 5258

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 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-eu 2048  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-rex 2481  df-v 2765  df-sbc 2990  df-un 3161  df-sn 3628  df-pr 3629  df-uni 3840  df-iota 5219  df-fv 5266

This theorem is referenced by: (None)