MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.44 Unicode version

Theorem 19.44 1815
Description: Theorem 19.44 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.44.1  |-  F/ x ps
Assertion
Ref Expression
19.44  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  ps ) )

Proof of Theorem 19.44
StepHypRef Expression
1 19.43 1593 . 2  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  E. x ps ) )
2 19.44.1 . . . 4  |-  F/ x ps
3219.9 1785 . . 3  |-  ( E. x ps  <->  ps )
43orbi2i 507 . 2  |-  ( ( E. x ph  \/  E. x ps )  <->  ( E. x ph  \/  ps )
)
51, 4bitri 242 1  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    \/ wo 359   E.wex 1529   F/wnf 1532
This theorem is referenced by:  eeor  1828  grothprim  8452
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  ax-6 1704  ax-11 1716
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-ex 1530  df-nf 1533
  Copyright terms: Public domain W3C validator