ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simp3rl GIF version

Theorem simp3rl 988
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3rl ((𝜃𝜏 ∧ (𝜒 ∧ (𝜑𝜓))) → 𝜑)

Proof of Theorem simp3rl
StepHypRef Expression
1 simprl 491 . 2 ((𝜒 ∧ (𝜑𝜓)) → 𝜑)
213ad2ant3 938 1 ((𝜃𝜏 ∧ (𝜒 ∧ (𝜑𝜓))) → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  prarloc  6658
  Copyright terms: Public domain W3C validator