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

Theorem biorf 650
Description: A wff is equivalent to its disjunction with falsehood. Theorem *4.74 of [WhiteheadRussell] p. 121. (Contributed by NM, 23-Mar-1995.) (Proof shortened by Wolf Lammen, 18-Nov-2012.)
Assertion
Ref Expression
biorf φ → (ψ ↔ (φ ψ)))

Proof of Theorem biorf
StepHypRef Expression
1 olc 619 . 2 (ψ → (φ ψ))
2 orel1 631 . 2 φ → ((φ ψ) → ψ))
31, 2impbid2 131 1 φ → (ψ ↔ (φ ψ)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 98   wo 616
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 533  ax-io 617
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  biortn  651  pm5.61  695  pm5.55dc  812  euor  1908  eueq3dc  2692  difprsnss  3476  opthprc  4318  frecsuclem3  5906  swoord1  6046  enq0tr  6289
  Copyright terms: Public domain W3C validator