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Theorem 19.3v 1654
Description: Special case of Theorem 19.3 of [Margaris] p. 89. (Contributed by NM, 1-Aug-2017.) (Revised by Wolf Lammen to remove dependency on ax-8, 4-Dec-2017.)
Assertion
Ref Expression
19.3v  |-  ( A. x ph  <->  ph )
Distinct variable group:    ph, x

Proof of Theorem 19.3v
StepHypRef Expression
1 alex 1562 . 2  |-  ( A. x ph  <->  -.  E. x  -.  ph )
2 19.9v 1653 . . 3  |-  ( E. x  -.  ph  <->  -.  ph )
32con2bii 322 . 2  |-  ( ph  <->  -. 
E. x  -.  ph )
41, 3bitr4i 243 1  |-  ( A. x ph  <->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176   A.wal 1530   E.wex 1531
This theorem is referenced by:  spvw  1655  19.9vOLD  1682
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
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