Theorem fv2 5553

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 5266	. 2 |- ( F ` A ) = ( iota y A F y )
2		dfiota2 5220	. 2 |- ( iota y A F y ) = U. { x | A. y ( A F y <-> y = x ) }
3	1, 2	eqtri 2217	1 |- ( F ` A ) = U. { x | A. y ( A F y <-> y = x ) }

Syntax hints:   <-> wb 105   A.wal 1362   = wceq 1364   {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-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-rex 2481  df-sn 3628  df-uni 3840  df-iota 5219  df-fv 5266

This theorem is referenced by:  elfv  5556