ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simprl3 GIF version

Theorem simprl3 990
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simprl3 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜒)

Proof of Theorem simprl3
StepHypRef Expression
1 simpl3 948 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜒)
21adantl 271 1 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  w3a 924
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 926
This theorem is referenced by:  prarloc  7062  icodiamlt  10613  isummo  10773
  Copyright terms: Public domain W3C validator