MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.39 Unicode version

Theorem 19.39 1673
Description: Theorem 19.39 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
19.39  |-  ( ( E. x ph  ->  E. x ps )  ->  E. x ( ph  ->  ps ) )

Proof of Theorem 19.39
StepHypRef Expression
1 19.2 1672 . . 3  |-  ( A. x ph  ->  E. x ph )
21imim1i 56 . 2  |-  ( ( E. x ph  ->  E. x ps )  -> 
( A. x ph  ->  E. x ps )
)
3 19.35 1588 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  E. x ps )
)
42, 3sylibr 205 1  |-  ( ( E. x ph  ->  E. x ps )  ->  E. x ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1528   E.wex 1529
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1312  df-fal 1313  df-ex 1530
  Copyright terms: Public domain W3C validator