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

Theorem biorfi 664
Description: A wff is equivalent to its disjunction with falsehood. (Contributed by NM, 23-Mar-1995.)
Hypothesis
Ref Expression
biorfi.1 ¬ φ
Assertion
Ref Expression
biorfi (ψ ↔ (ψ φ))

Proof of Theorem biorfi
StepHypRef Expression
1 biorfi.1 . 2 ¬ φ
2 orc 632 . . 3 (ψ → (ψ φ))
3 orel2 644 . . 3 φ → ((ψ φ) → ψ))
42, 3impbid2 131 . 2 φ → (ψ ↔ (ψ φ)))
51, 4ax-mp 7 1 (ψ ↔ (ψ φ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 98   wo 628
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 545  ax-io 629
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm4.43  855  dn1dc  866  excxor  1268  un0  3245  opthprc  4334  frec0g  5922  dcdc  9236
  Copyright terms: Public domain W3C validator