MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.19 Unicode version

Theorem 19.19 1867
Description: Theorem 19.19 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.19.1  |-  F/ x ph
Assertion
Ref Expression
19.19  |-  ( A. x ( ph  <->  ps )  ->  ( ph  <->  E. x ps ) )

Proof of Theorem 19.19
StepHypRef Expression
1 19.19.1 . . 3  |-  F/ x ph
2119.9 1784 . 2  |-  ( E. x ph  <->  ph )
3 exbi 1581 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( E. x ph  <->  E. x ps ) )
42, 3syl5bbr 250 1  |-  ( A. x ( ph  <->  ps )  ->  ( ph  <->  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1540   E.wex 1541   F/wnf 1544
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545
  Copyright terms: Public domain W3C validator