ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  19.45 Unicode version

Theorem 19.45 1616
Description: Theorem 19.45 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)
Hypothesis
Ref Expression
19.45.1  |-  F/ x ph
Assertion
Ref Expression
19.45  |-  ( E. x ( ph  \/  ps )  <->  ( ph  \/  E. x ps ) )

Proof of Theorem 19.45
StepHypRef Expression
1 19.43 1562 . 2  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  E. x ps ) )
2 19.45.1 . . . 4  |-  F/ x ph
3219.9 1578 . . 3  |-  ( E. x ph  <->  ph )
43orbi1i 713 . 2  |-  ( ( E. x ph  \/  E. x ps )  <->  ( ph  \/  E. x ps )
)
51, 4bitri 182 1  |-  ( E. x ( ph  \/  ps )  <->  ( ph  \/  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 103    \/ wo 662   F/wnf 1392   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-io 663  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  df-nf 1393
This theorem is referenced by:  eeor  1628
  Copyright terms: Public domain W3C validator