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

Theorem biorfi 698
Description: A wff is equivalent to its disjunction with falsehood. (Contributed by NM, 23-Mar-1995.)
Hypothesis
Ref Expression
biorfi.1  |-  -.  ph
Assertion
Ref Expression
biorfi  |-  ( ps  <->  ( ps  \/  ph )
)

Proof of Theorem biorfi
StepHypRef Expression
1 biorfi.1 . 2  |-  -.  ph
2 orc 666 . . 3  |-  ( ps 
->  ( ps  \/  ph ) )
3 orel2 678 . . 3  |-  ( -. 
ph  ->  ( ( ps  \/  ph )  ->  ps ) )
42, 3impbid2 141 . 2  |-  ( -. 
ph  ->  ( ps  <->  ( ps  \/  ph ) ) )
51, 4ax-mp 7 1  |-  ( ps  <->  ( ps  \/  ph )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 103    \/ wo 662
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-in2 578  ax-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  pm4.43  891  dn1dc  902  excxor  1310  un0  3279  opthprc  4411  frec0g  6040  dcdc  10708
  Copyright terms: Public domain W3C validator