Theorem tsna1

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

	Ref	Expression
Assertion	tsna1	|- ( th -> ( ( -. ph \/ -. ps ) \/ -. ( ph -/\ ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		tsan1	|- ( th -> ( ( -. ph \/ -. ps ) \/ ( ph /\ ps ) ) )
2		notnotb	|- ( ( ph -/\ ps ) <-> -. -. ( ph -/\ ps ) )
3		df-nan	|- ( ( ph -/\ ps ) <-> -. ( ph /\ ps ) )
4	2 3	bitr3i	|- ( -. -. ( ph -/\ ps ) <-> -. ( ph /\ ps ) )
5	4	con4bii	|- ( -. ( ph -/\ ps ) <-> ( ph /\ ps ) )
6	5	orbi2i	|- ( ( ( -. ph \/ -. ps ) \/ -. ( ph -/\ ps ) ) <-> ( ( -. ph \/ -. ps ) \/ ( ph /\ ps ) ) )
7	1 6	sylibr	|- ( th -> ( ( -. ph \/ -. ps ) \/ -. ( ph -/\ ps ) ) )