ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simp221 GIF version

Theorem simp221 1045
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp221 ((𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) ∧ 𝜁) → 𝜑)

Proof of Theorem simp221
StepHypRef Expression
1 simp21 937 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜑)
213ad2ant2 926 1 ((𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) ∧ 𝜁) → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 885
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 887
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator