Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  elfv Unicode version

Theorem elfv 5685
 Description: Membership in a function value. (Contributed by NM, 30-Apr-2004.)
Assertion
Ref Expression
elfv
Distinct variable groups:   ,   ,,   ,,
Allowed substitution hint:   ()

Proof of Theorem elfv
StepHypRef Expression
1 fv2 5682 . . 3
21eleq2i 2468 . 2
3 eluniab 3987 . 2
42, 3bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359  wal 1546  wex 1547   wcel 1721  cab 2390  cuni 3975   class class class wbr 4172  cfv 5413 This theorem is referenced by:  fv3  5703 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-rex 2672  df-v 2918  df-sn 3780  df-uni 3976  df-iota 5377  df-fv 5421
 Copyright terms: Public domain W3C validator