Users' Mathboxes Mathbox for Giovanni Mascellani < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  tsna2 Structured version   Visualization version   GIF version

Theorem tsna2 35304
Description: A Tseitin axiom for logical incompatibility, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)
Assertion
Ref Expression
tsna2 (𝜃 → (𝜑 ∨ (𝜑𝜓)))

Proof of Theorem tsna2
StepHypRef Expression
1 tsan2 35301 . 2 (𝜃 → (𝜑 ∨ ¬ (𝜑𝜓)))
2 df-nan 1476 . . 3 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
32orbi2i 906 . 2 ((𝜑 ∨ (𝜑𝜓)) ↔ (𝜑 ∨ ¬ (𝜑𝜓)))
41, 3sylibr 235 1 (𝜃 → (𝜑 ∨ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 396  wo 841  wnan 1475
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-nan 1476
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator