ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simp223 GIF version

Theorem simp223 1109
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp223 ((𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) ∧ 𝜁) → 𝜒)

Proof of Theorem simp223
StepHypRef Expression
1 simp23 1001 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜒)
213ad2ant2 988 1 ((𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) ∧ 𝜁) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 947
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 949
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator