ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simpl32 GIF version

Theorem simpl32 1048
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simpl32 (((𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜂) → 𝜓)

Proof of Theorem simpl32
StepHypRef Expression
1 simp32 1003 . 2 ((𝜃𝜏 ∧ (𝜑𝜓𝜒)) → 𝜓)
21adantr 274 1 (((𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜂) → 𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 947
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 949
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator