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

Theorem anandir 525
Description: Distribution of conjunction over conjunction. (Contributed by NM, 24-Aug-1995.)
Assertion
Ref Expression
anandir (((φ ψ) χ) ↔ ((φ χ) (ψ χ)))

Proof of Theorem anandir
StepHypRef Expression
1 anidm 376 . . 3 ((χ χ) ↔ χ)
21anbi2i 430 . 2 (((φ ψ) (χ χ)) ↔ ((φ ψ) χ))
3 an4 520 . 2 (((φ ψ) (χ χ)) ↔ ((φ χ) (ψ χ)))
42, 3bitr3i 175 1 (((φ ψ) χ) ↔ ((φ χ) (ψ χ)))
Colors of variables: wff set class
Syntax hints:   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  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  anandi3r  898  fununi  4910  imadiflem  4921  imadif  4922  imainlem  4923  elfzuzb  8614
  Copyright terms: Public domain W3C validator