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

Theorem ibir 177
Description: Inference that converts a biconditional implied by one of its arguments, into an implication. (Contributed by NM, 22-Jul-2004.)
Hypothesis
Ref Expression
ibir.1 (𝜑 → (𝜓𝜑))
Assertion
Ref Expression
ibir (𝜑𝜓)

Proof of Theorem ibir
StepHypRef Expression
1 ibir.1 . . 3 (𝜑 → (𝜓𝜑))
21bicomd 141 . 2 (𝜑 → (𝜑𝜓))
32ibi 176 1 (𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  pm5.21nii  704  elpr2  3615  eusv2i  4456  ffdm  5387  ov  5994  ovg  6013  nnacl  6481  elpm2r  6666  ltnqpri  7593  ltxrlt  8023  uzaddcl  9586  expcllem  10531  qexpclz  10541  1exp  10549  facnn  10707  fac0  10708  fac1  10709  bcn2  10744  znnen  12399
  Copyright terms: Public domain W3C validator