Users' Mathboxes Mathbox for Giovanni Mascellani < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  tsna3 Structured version   Unicode version

Theorem tsna3 32092
Description: A Tseitin axiom for logical incompatibility, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.)
Assertion
Ref Expression
tsna3  |-  ( th 
->  ( ps  \/  ( ph  -/\  ps ) ) )

Proof of Theorem tsna3
StepHypRef Expression
1 tsan3 32089 . 2  |-  ( th 
->  ( ps  \/  -.  ( ph  /\  ps )
) )
2 df-nan 1380 . . 3  |-  ( (
ph  -/\  ps )  <->  -.  ( ph  /\  ps ) )
32orbi2i 521 . 2  |-  ( ( ps  \/  ( ph  -/\ 
ps ) )  <->  ( ps  \/  -.  ( ph  /\  ps ) ) )
41, 3sylibr 215 1  |-  ( th 
->  ( ps  \/  ( ph  -/\  ps ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 369    /\ wa 370    -/\ wnan 1379
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 188  df-or 371  df-an 372  df-nan 1380
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator