ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  19.42 Unicode version

Theorem 19.42 1699
Description: Theorem 19.42 of [Margaris] p. 90. (Contributed by NM, 18-Aug-1993.)
Hypothesis
Ref Expression
19.42.1  |-  F/ x ph
Assertion
Ref Expression
19.42  |-  ( E. x ( ph  /\  ps )  <->  ( ph  /\  E. x ps ) )

Proof of Theorem 19.42
StepHypRef Expression
1 19.42.1 . . 3  |-  F/ x ph
2119.41 1697 . 2  |-  ( E. x ( ps  /\  ph )  <->  ( E. x ps  /\  ph ) )
3 exancom 1619 . 2  |-  ( E. x ( ph  /\  ps )  <->  E. x ( ps 
/\  ph ) )
4 ancom 266 . 2  |-  ( (
ph  /\  E. x ps )  <->  ( E. x ps  /\  ph ) )
52, 3, 43bitr4i 212 1  |-  ( E. x ( ph  /\  ps )  <->  ( ph  /\  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 104    <-> wb 105   F/wnf 1471   E.wex 1503
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-ial 1545
This theorem depends on definitions:  df-bi 117  df-nf 1472
This theorem is referenced by:  eean  1947  r2exf  2512
  Copyright terms: Public domain W3C validator