ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simp33r GIF version

Theorem simp33r 1069
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp33r ((𝜏𝜂 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜓)

Proof of Theorem simp33r
StepHypRef Expression
1 simp3r 970 . 2 ((𝜒𝜃 ∧ (𝜑𝜓)) → 𝜓)
213ad2ant3 964 1 ((𝜏𝜂 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  w3a 922
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 924
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator