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

Theorem biimpac 282
Description: Inference from a logical equivalence. (Contributed by NM, 3-May-1994.)
Hypothesis
Ref Expression
biimpa.1 (φ → (ψχ))
Assertion
Ref Expression
biimpac ((ψ φ) → χ)

Proof of Theorem biimpac
StepHypRef Expression
1 biimpa.1 . . 3 (φ → (ψχ))
21biimpcd 148 . 2 (ψ → (φχ))
32imp 115 1 ((ψ φ) → χ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  gencbvex2  2595  onsucelsucexmidlem  4214  ordsuc  4241  poltletr  4668  tz6.12-1  5143  nfunsn  5150  nnaordex  6036  th3qlem1  6144  ssfiexmid  6254  nqnq0pi  6421  distrlem1prl  6558  distrlem1pru  6559  eqle  6906
  Copyright terms: Public domain W3C validator