Theorem fv2 5594

Description: Alternate definition of function value. Definition 10.11 of [Quine] p. 68. (Contributed by NM, 30-Apr-2004.) (Proof shortened by Andrew Salmon, 17-Sep-2011.) (Revised by Mario Carneiro, 31-Aug-2015.)

Assertion

Ref	Expression
fv2	|- ( F ` A ) = U. { x | A. y ( A F y <-> y = x ) }

Distinct variable groups:   x, y, A   x, F, y

Proof of Theorem fv2

Step	Hyp	Ref	Expression
1		df-fv 5298	. 2 |- ( F ` A ) = ( iota y A F y )
2		dfiota2 5252	. 2 |- ( iota y A F y ) = U. { x | A. y ( A F y <-> y = x ) }
3	1, 2	eqtri 2228	1 |- ( F ` A ) = U. { x | A. y ( A F y <-> y = x ) }

Syntax hints:   <-> wb 105   A.wal 1371   = wceq 1373   {cab 2193   U.cuni 3864   class class class wbr 4059   iotacio 5249   ` cfv 5290

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-rex 2492  df-sn 3649  df-uni 3865  df-iota 5251  df-fv 5298

This theorem is referenced by:  elfv  5597