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Theorem 19.9v 1672
Description: Special case of Theorem 19.9 of [Margaris] p. 89. Revised to remove dependency on ax-8 1683. (Contributed by NM, 28-May-1995.) (Revised by NM, 1-Aug-2017.) (Revised by Wolf Lammen, 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 1625 . 2  |-  ( E. x ph  ->  ph )
2 ax-17 1623 . . 3  |-  ( ph  ->  A. x ph )
3219.8w 1668 . 2  |-  ( ph  ->  E. x ph )
41, 3impbii 181 1  |-  ( E. x ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 177   E.wex 1547
This theorem is referenced by:  19.3v  1673  exlimivOLD  1707  zfcndpow  8447  volfiniune  24539  prter2  26620  rfcnnnub  27574  relopabVD  28722  bnj937  28848  bnj594  28989  bnj907  29042  bnj1128  29065  bnj1145  29068
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
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548
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