ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm3.2ni GIF version

Theorem pm3.2ni 787
Description: Infer negated disjunction of negated premises. (Contributed by NM, 4-Apr-1995.)
Hypotheses
Ref Expression
pm3.2ni.1 ¬ 𝜑
pm3.2ni.2 ¬ 𝜓
Assertion
Ref Expression
pm3.2ni ¬ (𝜑𝜓)

Proof of Theorem pm3.2ni
StepHypRef Expression
1 pm3.2ni.1 . 2 ¬ 𝜑
2 id 19 . . 3 (𝜑𝜑)
3 pm3.2ni.2 . . . 4 ¬ 𝜓
43pm2.21i 620 . . 3 (𝜓𝜑)
52, 4jaoi 690 . 2 ((𝜑𝜓) → 𝜑)
61, 5mto 636 1 ¬ (𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wo 682
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589  ax-io 683
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  xrltnr  9534  pnfnlt  9541  nltmnf  9542
  Copyright terms: Public domain W3C validator