ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simpll1 GIF version

Theorem simpll1 954
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simpll1 ((((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑)

Proof of Theorem simpll1
StepHypRef Expression
1 simpl1 918 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜑)
21adantr 265 1 ((((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  fidifsnen  6362  ordiso2  6415  addlocpr  6692  expival  9422
  Copyright terms: Public domain W3C validator