NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  anandir GIF version

Theorem anandir 802
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 625 . . 3 ((χ χ) ↔ χ)
21anbi2i 675 . 2 (((φ ψ) (χ χ)) ↔ ((φ ψ) χ))
3 an4 797 . 2 (((φ ψ) (χ χ)) ↔ ((φ χ) (ψ χ)))
42, 3bitr3i 242 1 (((φ ψ) χ) ↔ ((φ χ) (ψ χ)))
Colors of variables: wff setvar class
Syntax hints:  wb 176   wa 358
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360
This theorem is referenced by:  cadan  1392  fununi  5160  imadif  5171  restxp  5786
  Copyright terms: Public domain W3C validator