ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simpr22 GIF version

Theorem simpr22 1034
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simpr22 ((𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜓)

Proof of Theorem simpr22
StepHypRef Expression
1 simp22 980 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜓)
21adantl 272 1 ((𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 927
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 929
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator