ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simpr33 GIF version

Theorem simpr33 1089
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simpr33 ((𝜂 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜒)

Proof of Theorem simpr33
StepHypRef Expression
1 simp33 1035 . 2 ((𝜃𝜏 ∧ (𝜑𝜓𝜒)) → 𝜒)
21adantl 277 1 ((𝜂 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 980
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator