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Theorem 19.25 1560
Description: Theorem 19.25 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 2-Feb-2015.)
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 19.35-1 1558 . . 3  |-  ( E. x ( ph  ->  ps )  ->  ( A. x ph  ->  E. x ps ) )
21alimi 1387 . 2  |-  ( A. y E. x ( ph  ->  ps )  ->  A. y
( A. x ph  ->  E. x ps )
)
3 exim 1533 . 2  |-  ( A. y ( A. x ph  ->  E. x ps )  ->  ( E. y A. x ph  ->  E. y E. x ps ) )
42, 3syl 14 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 1285   E.wex 1424
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-ial 1470
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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