MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.9v Unicode version

Theorem 19.9v 1653
Description: Special case of Theorem 19.9 of [Margaris] p. 89. (Contributed by NM, 28-May-1995.) (Revised by NM, 1-Aug-2017.) (Revised by Wolf Lammen to remove dependency on ax-8, 4-Dec-2017.)
Assertion
Ref Expression
19.9v  |-  ( E. x ph  <->  ph )
Distinct variable group:    ph, x

Proof of Theorem 19.9v
StepHypRef Expression
1 ax17e 1608 . 2  |-  ( E. x ph  ->  ph )
2 ax-17 1606 . . 3  |-  ( ph  ->  A. x ph )
3219.8w 1649 . 2  |-  ( ph  ->  E. x ph )
41, 3impbii 180 1  |-  ( E. x ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 176   E.wex 1531
This theorem is referenced by:  19.3v  1654  exlimivOLD  1683  zfcndpow  8254  prter2  26852  rfcnnnub  27810  relopabVD  28993  bnj937  29119  bnj594  29260  bnj907  29313  bnj1128  29336  bnj1145  29339
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532
  Copyright terms: Public domain W3C validator