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Theorem 19.37 2056
Description: Theorem 19.37 of [Margaris] p. 90. See 19.37v 1836 for a version requiring fewer axioms. (Contributed by NM, 21-Jun-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 1750 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  E. x ps )
)
2 19.37.1 . . . 4  |-  F/ x ph
3219.3 1976 . . 3  |-  ( A. x ph  <->  ph )
43imbi1i 331 . 2  |-  ( ( A. x ph  ->  E. x ps )  <->  ( ph  ->  E. x ps )
)
51, 4bitri 257 1  |-  ( E. x ( ph  ->  ps )  <->  ( ph  ->  E. x ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 189   A.wal 1452   E.wex 1673   F/wnf 1677
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-12 1943
This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1674  df-nf 1678
This theorem is referenced by:  bnj900  29788
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