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Theorem 19.37-1 1635
Description: One direction of Theorem 19.37 of [Margaris] p. 90. The converse holds in classical logic but not, in general, here. (Contributed by Jim Kingdon, 21-Jun-2018.)
Hypothesis
Ref Expression
19.37-1.1  |-  F/ x ph
Assertion
Ref Expression
19.37-1  |-  ( E. x ( ph  ->  ps )  ->  ( ph  ->  E. x ps )
)

Proof of Theorem 19.37-1
StepHypRef Expression
1 19.37-1.1 . . 3  |-  F/ x ph
2119.3 1516 . 2  |-  ( A. x ph  <->  ph )
3 19.35-1 1586 . 2  |-  ( E. x ( ph  ->  ps )  ->  ( A. x ph  ->  E. x ps ) )
42, 3syl5bir 152 1  |-  ( E. x ( ph  ->  ps )  ->  ( ph  ->  E. x ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1312   F/wnf 1419   E.wex 1451
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 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-ial 1497
This theorem depends on definitions:  df-bi 116  df-nf 1420
This theorem is referenced by:  19.37aiv  1636  spcimegft  2736  eqvincg  2781
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