Metamath Proof Explorer

Theorem tsna2

Description: A Tseitin axiom for logical incompatibility, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018)

Ref Expression
Assertion tsna2 
|- ( th -> ( ph \/ ( ph -/\ ps ) ) )

Proof

Step Hyp Ref Expression
1 tsan2 
 |-  ( th -> ( ph \/ -. ( ph /\ ps ) ) )
2 df-nan 
 |-  ( ( ph -/\ ps ) <-> -. ( ph /\ ps ) )
3 2 orbi2i 
 |-  ( ( ph \/ ( ph -/\ ps ) ) <-> ( ph \/ -. ( ph /\ ps ) ) )
4 1 3 sylibr 
 |-  ( th -> ( ph \/ ( ph -/\ ps ) ) )