ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simpl3l GIF version

Theorem simpl3l 1036
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simpl3l (((𝜒𝜃 ∧ (𝜑𝜓)) ∧ 𝜏) → 𝜑)

Proof of Theorem simpl3l
StepHypRef Expression
1 simp3l 1009 . 2 ((𝜒𝜃 ∧ (𝜑𝜓)) → 𝜑)
21adantr 274 1 (((𝜒𝜃 ∧ (𝜑𝜓)) ∧ 𝜏) → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 962
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 964
This theorem is referenced by:  tfisi  4501  ltmul1a  8367  ltmul1  8368  lemul1a  8630  xaddass  9666  dvdsadd2b  11553
  Copyright terms: Public domain W3C validator