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Theorem 19.19 1644
Description: Theorem 19.19 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)
Hypothesis
Ref Expression
19.19.1  |-  F/ x ph
Assertion
Ref Expression
19.19  |-  ( A. x ( ph  <->  ps )  ->  ( ph  <->  E. x ps ) )

Proof of Theorem 19.19
StepHypRef Expression
1 19.19.1 . . 3  |-  F/ x ph
2119.9 1623 . 2  |-  ( E. x ph  <->  ph )
3 exbi 1583 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( E. x ph  <->  E. x ps ) )
42, 3bitr3id 193 1  |-  ( A. x ( ph  <->  ps )  ->  ( ph  <->  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1329   F/wnf 1436   E.wex 1468
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-ial 1514
This theorem depends on definitions:  df-bi 116  df-nf 1437
This theorem is referenced by: (None)
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