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Theorem fv2 5324
 Description: Alternate definition of function value. Definition 10.11 of [Quine] p. 68. (The proof was shortened by Andrew Salmon, 17-Sep-2011.) (Contributed by set.mm contributors, 30-Apr-2004.) (Revised by set.mm contributors, 18-Sep-2011.)
Assertion
Ref Expression
fv2 (FA) = {x y(AFyy = x)}
Distinct variable groups:   x,y,A   x,F,y

Proof of Theorem fv2
StepHypRef Expression
1 df-fv 4795 . 2 (FA) = (℩yAFy)
2 dfiota2 4340 . 2 (℩yAFy) = {x y(AFyy = x)}
31, 2eqtri 2373 1 (FA) = {x y(AFyy = x)}
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176  ∀wal 1540   = wceq 1642  {cab 2339  ∪cuni 3891  ℩cio 4337   class class class wbr 4639   ‘cfv 4781 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-sn 3741  df-uni 3892  df-iota 4339  df-fv 4795 This theorem is referenced by:  elfv  5326
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