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Theorem 19.25 1593
Description: Theorem 19.25 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
19.25  |-  ( A. y E. x ( ph  ->  ps )  ->  ( E. y A. x ph  ->  E. y E. x ps ) )

Proof of Theorem 19.25
StepHypRef Expression
1 19.35 1590 . . . 4  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  E. x ps )
)
21biimpi 186 . . 3  |-  ( E. x ( ph  ->  ps )  ->  ( A. x ph  ->  E. x ps ) )
32alimi 1549 . 2  |-  ( A. y E. x ( ph  ->  ps )  ->  A. y
( A. x ph  ->  E. x ps )
)
4 exim 1565 . 2  |-  ( A. y ( A. x ph  ->  E. x ps )  ->  ( E. y A. x ph  ->  E. y E. x ps ) )
53, 4syl 15 1  |-  ( A. y E. x ( ph  ->  ps )  ->  ( E. y A. x ph  ->  E. y E. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530   E.wex 1531
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532
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