ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simprl2 GIF version

Theorem simprl2 961
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simprl2 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜓)

Proof of Theorem simprl2
StepHypRef Expression
1 simpl2 919 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜓)
21adantl 266 1 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜓)
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  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  prarloc  6658  icodiamlt  9999
  Copyright terms: Public domain W3C validator