ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  mooran1 Unicode version

Theorem mooran1 2015
Description: "At most one" imports disjunction to conjunction. (Contributed by NM, 5-Apr-2004.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)
Assertion
Ref Expression
mooran1  |-  ( ( E* x ph  \/  E* x ps )  ->  E* x ( ph  /\  ps ) )

Proof of Theorem mooran1
StepHypRef Expression
1 simpl 107 . . 3  |-  ( (
ph  /\  ps )  ->  ph )
21moimi 2008 . 2  |-  ( E* x ph  ->  E* x ( ph  /\  ps ) )
3 moan 2012 . 2  |-  ( E* x ps  ->  E* x ( ph  /\  ps ) )
42, 3jaoi 669 1  |-  ( ( E* x ph  \/  E* x ps )  ->  E* x ( ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    \/ wo 662   E*wmo 1944
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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-eu 1946  df-mo 1947
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator