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Theorem 19.37 1790
Description: Theorem 19.37 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.37.1  |-  F/ x ph
Assertion
Ref Expression
19.37  |-  ( E. x ( ph  ->  ps )  <->  ( ph  ->  E. x ps ) )

Proof of Theorem 19.37
StepHypRef Expression
1 19.35 1599 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  E. x ps )
)
2 19.37.1 . . . 4  |-  F/ x ph
3219.3 1760 . . 3  |-  ( A. x ph  <->  ph )
43imbi1i 317 . 2  |-  ( ( A. x ph  ->  E. x ps )  <->  ( ph  ->  E. x ps )
)
51, 4bitri 242 1  |-  ( E. x ( ph  ->  ps )  <->  ( ph  ->  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178   A.wal 1532   E.wex 1537   F/wnf 1539
This theorem is referenced by:  19.37v  2033  bnj900  28010
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540
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