ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simp32 GIF version

Theorem simp32 952
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
Assertion
Ref Expression
simp32 ((𝜑𝜓 ∧ (𝜒𝜃𝜏)) → 𝜃)

Proof of Theorem simp32
StepHypRef Expression
1 simp2 916 . 2 ((𝜒𝜃𝜏) → 𝜃)
213ad2ant3 938 1 ((𝜑𝜓 ∧ (𝜒𝜃𝜏)) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  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:  simpl32  997  simpr32  1006  simp132  1051  simp232  1060  simp332  1069
  Copyright terms: Public domain W3C validator