ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simp-4l GIF version

Theorem simp-4l 508
Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.)
Assertion
Ref Expression
simp-4l (((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑)

Proof of Theorem simp-4l
StepHypRef Expression
1 simplll 500 . 2 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜑)
21adantr 270 1 (((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102
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 is referenced by:  simp-5l  510  fnfi  6479  sumeq2  10416
  Copyright terms: Public domain W3C validator