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

Theorem simplll 734
Description: Simplification of a conjunction. (Contributed by Jeff Hankins, 28-Jul-2009.)
Assertion
Ref Expression
simplll ((((φ ψ) χ) θ) → φ)

Proof of Theorem simplll
StepHypRef Expression
1 simpl 443 . 2 ((φ ψ) → φ)
21ad2antrr 706 1 ((((φ ψ) χ) θ) → φ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   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:  simp-4l  742  prepeano4  4451  nnpw1ex  4484  tfindi  4496  evenodddisj  4516  enprmaplem3  6078
  Copyright terms: Public domain W3C validator