ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm5.19 GIF version

Theorem pm5.19 657
Description: Theorem *5.19 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.) (Revised by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
pm5.19 ¬ (𝜑 ↔ ¬ 𝜑)

Proof of Theorem pm5.19
StepHypRef Expression
1 bi1 116 . . . 4 ((𝜑 ↔ ¬ 𝜑) → (𝜑 → ¬ 𝜑))
21pm2.01d 583 . . 3 ((𝜑 ↔ ¬ 𝜑) → ¬ 𝜑)
3 id 19 . . 3 ((𝜑 ↔ ¬ 𝜑) → (𝜑 ↔ ¬ 𝜑))
42, 3mpbird 165 . 2 ((𝜑 ↔ ¬ 𝜑) → 𝜑)
54, 2pm2.65i 603 1 ¬ (𝜑 ↔ ¬ 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  pm5.16  773  pclem6  1310  pm5.18im  1321  ru  2839
  Copyright terms: Public domain W3C validator